As a player who has a background in Mouse Guard, D&D 3.5 and 4e, oWoD, Call of Cthulhu and Fallout, what should I know about Shadowrun 4th edition? What is different about it in comparison to the RPGs I listed above? If I suggest playing it with friends, how should I describe the world and gameplay of it? Also, what are the key tropes and features, unique or not, of the system in regards to gameplay?
I haven't played Mouse Guard or Cthulhu, but I can comment on how the game plays out. Understand, however, that you can play it however you want once you get to know the game mechanics.
The focus of the game is less on acquiring treasure or experience points or even getting political respect. It's much more about living from day to day on meager paychecks you get for illegal acts of terrorism, violence, or whatever flavor of criminal activity the Story Teller has up their sleeve at the time. Your focus is on paying your bills, apartment rent, and getting better toys to do better runs to stay alive longer. It's a commonly held belief in the story of the game that if you're a Shadowrunner and you've lived for more then 5 years doing runs, you're a veteran... because the job has a high mortality rate.
I liken this very much to the flavor you'll get out of oWoD. Because of the way the stats are set up, many conflicts are resolved through smooth talking, diplomacy, and then the occasional use of a power. While in D&D, it's very much centered on what your character can do and pointing them at that problem, Shadowrun is a group effort. While the big, bad troll with a Vindicator Chaingun doesn't have high social skills, he's still expected to be a part of the story telling and that's where much of the fun of the game comes in. Also, with the story, much of this happens in a futuristic Seattle when there is no USA, but broken factions and corporations. That's not to say that it's not relate-able. You still see cars, TV, movies, music, and social media being at play, so it's much easier for people new to Sci-Fi and Fantasy to get into.
As far as the gameplay goes, this is one of the bigger aspects of the game that, in my opinion, detracts from other games. The core material suggests that you will get into combat. A lot. They give you a lot of combat material to sift through, and drones to rig, magic to sling around, and entire books dedicated to weapons. So you will be getting into combat, that's not a question. Where it differs from heavy combat RPGs (such as D&D) is that it doesn't EXPECT you to get into combat. That is the DM's call and the PC's call.
We call this scale the Pink Mohawk/Black Shades scale. Shadowrun can be broken down with it's action and combat into either a gun fest where bullets are slung around and explosions go off every game, or into stealth and guile, using your wit and professionalism to get the job done without pulling a trigger and only having that gun on you as a last resort. It's up to the players and ST to determine what is good for the group. The way that combat evolves from it can be either tactical or Mind's Theater (much like in oWoD where you don't have a battle mat)
As a last comment, I think the biggest selling point of Shadowrun and what puts it apart from other is that you can make whatever you want. A cyborg, a gun bunny, a face, a magical anime girl. Anything. It's a very, very versatile system and it opens many possibilities.
Can't comment on oWoD, CoC, or fallout.
It's not as structured as 4e but definitely has more expectation of play then 3.5. Tropes if you will. Like Mouseguard, its expects the DM to throw certain things at the players. Instead of weather and predictors, it's back-stabbing clients and bad intel. It also expects the players to perform a certain role. Instead of building up mouse-kind, it's shoot people in the face for money.
If you imagined a 3.5 game set in an urban environment and you're part of a thieves/assassins guild, then you'd have a game very similar to shadowrun. Minus computers, and firearms. Magic, magic (equivalent) items, and people with super-human skills still exist. I saw a guy gun down a tank with an SMG. Net hits can act funky.
The math is a little different, but it's not too bad. One thing that you should be aware of is that it can involve multiple planes of existence. In addition to the real world, there's matrix space, and astral space. Only the hackers play in the matrix, and only wizards play on the astral. While it was a cool idea, it means that more then half the party is bored while the special guy gets his time in his own dimension. Starting out, I'd disallow any matrix users, spell casters, or riggers. Just to simplify things.
Explain the setting this way:
It's a dystopian high-tech future where corporations have risen above national powers. They're sovereign in their own turf and run most of the world in a very direct way. There have been massive catastrophes, political upheaval, and freaky deaky fantasy stuff (if you feel like including that part). But there has been technological progress; the Internet and gadgets are ubiquitous. We've developed space. And the human lifespan can be extended greatly... if you can afford it.
The role of the players:
But you're not (usually) up there living the high life with semi-immortal space CEOs. You're down here in the gutters trying to scrap by. Shadowrun revolves around criminal enterprise. You are criminals being paid to perform illegal activities. Although, "illegal" is more fuzzy now-a-days, as even the cops are for-profit corporations and legality is usually tied to someone's profit margin. But in the free-market orgy that is corporate rule, they often need plausible deniability for overly-competitive use of explosives, and shadow runners fit the bill. And in a dystopian world, there are plenty of opportunities for those willing to bend the rules and/or shoot people in the face.