I think your question can mostly be reduced to…
1. How do their basic mechanics and resolution systems compare?
All three games are fairly "traditional" — they're built around task-focused resolution and assume players will spend most of their time in actor stance.
Basic resolution:
Rolling dice in V20 is a little more complicated because target numbers can fluctuate — VTR2 and V5 both use a fixed target number (e.g. every 8 or higher on a d10 counts as 1 success in your pool), which makes it easier to develop intuition about probabilities after a few session.
V5 also adds a bit of complexity to rolls with "hunger dice," but this is a mechanic that replaces bookkeeping associated with tracking blood points in the other two systems. (All three still have health and willpower scores that will fluctuate during the session.)
Stuff on your character sheet:
All three games represent characters as a combination of attribute scores, skills, disciplines (specialized vampiric powers), and merits (sort of a "miscellaneous" category that includes reputation, unusual personal qualities, unique fighting styles, useful minions, &c).
Of the three games, Requiem 2nd Edition has the clearest discipline write-ups — the first-tier power tends to be thematic and powerful in its own right, and dots 2-5 tend to expand on it in various ways. V20 devotes a lot of page count to rare and quirky stuff like elder-only powers, clan-specific powers for barely-there clans, and vampire magic that falls well outside of the central theme of each style (like a water-themed Thaumaturgy sub-school). V5 sort of straddles the border, with complexity closer to VTR2's but less focus and (in my opinion) polish.
One downside of VTR2 is that the blood magic in the core book is a little too bare — it's unclear how to make use of some of the powers productively, and a campaign where someone actually plays a dedicated magic-user is probably going to involve at least one of 1e Blood Sorcery (for its complex DIY magic system, mostly compatible with the 2e core) or 2e Secrets of the Covenants (for its additional pre-built spells to fill in central things a sorcerer of the appropriate faction would want to do) to fill in the gaps. If you're looking to play a vampiric mage figure, I think V5 core's Thaumaturgy and Thin-Blood Alchemy are closest to being well-detailed but manageably complex "out of the box."
VTR2 also has slightly deeper non-discipline-based customization options for combat characters, in the form of Combat Style merits drawn from Chronicles of Darkness 2nd Edition (the relevant excerpts are distributed as a free PDF), Hurt Locker, or Secrets of the Covenants.
In my experience, the stat numbers are simple enough that "eyeballing" an NPC's stats on the spot isn't too hard for a GM — if you mess up, it's likely because of discipline interactions rather than raw stat+skill numbers, and I think all three games have about the same risk of that.
2. What "narrative" mechanics does each game employ?
Humanity subsystems:
A major feature of every edition of both the Vampire: the Masquerade and Vampire: the Requiem game lines is the Humanity subsystem, representing a vampire's connection to mortal emotional and moral patterns. These are fairly "intrusive" mechanics that tend to be the centerpiece of the "personal horror" aspect of the games. Humanity is supposed to promote introspection and signpost your character's spiral into monstrousness, or their valiant struggle to stay connected with their better nature. It's a big part of what makes a Vampire game a Vampire game.
And, quite frankly, I think every Vampire game has messed up the actual mechanical implementation of it super hard, with only one exception, and that's Requiem 2nd Edition (not 1st Edition). And that's because it's the only game that engages with Humanity in terms of alienation rather than morality. It's a subtle difference but a big change in play. The result is that you don't have to fuss over questions of good and evil, crime and sin and justification, &c. at the table because a mechanic asked you to. Those questions may be important in play, but in my experience they're better when we don't have to make a pseudo-"objective" determination here and now as part of a die roll. (Rather, the thing that matters mechanically in the moment is trauma.) All of this suits the game's "Southern gothic" vibe rather well, in my opinion.
Requiem 2e is also a game that rewards you for facing detachment rather than treating Humanity loss as a near-totally punitive thing. Which means there's actually an incentive for players to push towards the theme rather than avoid it. In my experience, this leads to more direct engagement with Humanity than in its other formulations.
I'm pointing this out not so much to assert that VTR2 is flat-out better, but to spotlight its approach because I think other Vampire games can be easily improved by transplanting it there as well.
That said, V20 does have something interesting you won't find in the other two games: "Paths of Enlightenment." These represent vampires' attempts to construct new moral/psychological codes specific to their natures. Playing around with these inhuman philosophies and faiths can be great fun, and some players appreciate having the explicit mechanical structure for them.
V5's useful contribution is that it asks you to figure out the specific genre of your game, and build a list of moral tenets around that. This ties the moral struggle more closely to a few specific themes rather than a one-size-fits-all approach like older VtM games.
VTR2 and V5 are both notable for moving their respective Humanity systems away from "derangements," which is an unfortunate bit of the older games that attaches a rather clunky and caricatured take on mental illness to the characters' declining Humanity.
Moment-to-moment narrative mechanics:
V5 aims to put vampiric urges front and center with its "Hunger" mechanic, which adds a risk of messy consequences to every important die roll. (All Vampire games include a frenzy mechanic wherein certain situations could cause loss of self-control to the Beast, but Hunger is more of a "narrative"/"indie-style" mechanic that produces unexpected twists and a feeling of tension without jerking the PCs around as much as constant frenzy checks would.)
VTR2 puts a lot of emphasis on Conditions, which represent "ways in which the story has affected your character, and what she can do to move past those events." That's a broad category of stuff ranging from strong emotions, to physical issues (addiction, e.g.), to another vampire's powers messing with your mind. They're structured to encourage you to "lean into" roleplaying your reactions when bad stuff happens (by giving you XP), or to define clear mechanical triggers and limits to certain narrative events that constrain your actions and options. I like the general flow these promote, but they do tend to be "heavier" than similar bribing-you-to-lean-into-the-bad-stuff mechanics you'll see in games like Apocalypse World.
3. How does each game structure the delivery of its setting/lore?
The two Masquerade games present the same setting at slightly different stages in its evolution. V20 is a massive omnibus book that tries to give you a condensed but comprehensive version of 20 years of the roleplaying game — all the clans, all the paths, rare ritual forms and elder disciplines. The core book itself doesn't contain all the historical or geographical details, but it does provide a fairly comprehensive structure for making sense of information in a separate city book you bought, or stuff you find while browsing the White Wolf Wiki.
V5 instead pares down the setting a bit by introducing new events that shake up the axes of power — the ancients and elders are more removed from the characters' daily struggles, so you can afford to detail them less, that kind of thing. The core book is a bit of a "slimmed down" view of the setting — it only presents mechanics for seven of the thirteen clans while gently referencing the rest, for example; the clan write-ups and loresheets allude to setting metaplot stuff that isn't explained in the book. You can figure it all out with a few extra books (I think Beckett's Jyhad Diary is the recommended one, until V5 actually gets its own set of supplements) or a lot of time on the White Wolf Wiki — or you can let the dangling hooks stay dangling, if you're comfortable picking and choosing from a game's established "canon."
Requiem handles setting material a bit differently. As a game line, it's far less concerned with metaplot or a big overarching canon. The intent of the core book is to be all the setting material you need — there are more ideas you can use in the 1st-edition clan books or 2nd edition's Secrets of the Covenants — often presents as tidbits of fiction "in character" — but all of it is quite optional and more focused on giving you story ideas than presenting an expansive, consistent whole-world setting. (Most of the Onyx Path "fluff" material is self-consistent, you're just not expected to cross-check your own game against it to ensure correctness. Oftentimes, I feel like it's more concerned with setting the mood than giving you explicit setting material to work with.)
Of the three games' core books, I'd say Requiem 2nd Edition is the most self-contained: the core book explains all the clans and covenants (political groupings), and offer a large section devoted to different cities representing unique cultural and political environments. Because the Requiem setting's vampire politics explicitly revolves around political groups and local personalities (that you're inventing in play), rather than the allegiances of entire clans based on the machinations and rivalries of powerful elders playing out on the global stage, how it all fits together tends to be rather straightforward.
Of course, one of the benefits of VtM over VtR is that there's more "side channel" ways to learn about the setting, such as the Bloodlines video game. You may find a lot of folks already know some details (and have imagined VtM characters they'd like to play) even if they've never touched pen-and-paper VtM itself.
Streamlining and system hacking
I feel like this needs its own section, because it's relevant to the question of streamlining and improvisation: Requiem 2nd Edition has a fairly large section (in Chapter 7: Storytelling) devoted to simplifying the mechanics in various ways to produce a particular result. The other systems can be tweaked this way as well, but the Requiem 2nd Edition core book definitely offers more guidance and support for it as a text.
The advice does tend to be rather "scorched earth," however: more like how to turn VTR2 into freeform with 1-2 guiding mechanics than how to tweak the basic engine in subtle ways.
