I have two observations, which don’t strictly have anything to do with the spellbook per se, but rather about the context in which the wizard exists, and then I’ll note a number of advantages and disadvantages that the wizard has due to the spellbook.
Observation: the wizard is a “prepared caster”
The wizard casts spells by preparing a subset of those they have available each morning. This is different from some other spellcasters (sometimes called “spontaneous”), that simply know a fixed selection of spells and just casts those without preparation. Other prepared casters include the cleric and druid, and contrast with classes like bard or sorcerer.
Preparation is generally an advantage: you can choose spells relevant for that particular day, instead of having to choose spells that will be relevant for the rest of your life. Spontaneous spellcasters do get somewhat more spells known than a prepared caster can prepare on any given day, particularly at high levels, which mitigates this advantage somewhat, but in my experience preparation is still decidedly the better way to go. (In a vacuum; obviously every spellcasting class also has other potent features that mean you are never just picking “prepared” vs. “spontaneous.” This kind of “theoretical, in a vacuum comparison” vs. “contextual, in practice comparison” is a big theme with this anwer.)
Either way, though, it makes the most sense to compare the wizard’s spellcasting to the cleric and druid, since they’re the most comparable classes.
Observation: the wizard spell list is massive
The wizard’s spell list is simply a great deal larger than other classes’. That has a lot of influence over how we should look at how the wizard’s spellcasting works.
Disadvantage: no immediate access to the entire wizard spell list
Compared to other prepared casters—the aforementioned cleric and druid—the wizard has to jump through extra hoops to prepare their spells. Clerics and druids just get to prepare any and all cleric and druid spells, respectively, as soon as they reach the appropriate level.
The wizard cannot. The wizard has to get them into their spellbook first. They get a few for free as they level up, but the rest require time and money. That’s a drawback.
Note, however, that this directly goes to the advantage we observed previously: the wizard spell list is massive. That means that, while at first the wizard may not have immediate access to as many spells as a cleric or druid, if they are diligent about filling up their spellbook they can eventually gain access to many, many more spells.
If one had access to the wizard spell list, but didn’t have to worry about a spellbook, that would obviously be better. But that isn’t an option that the game is presenting. Instead, you have a trade-off: deal with a spellbook, and theoretically get access to a lot more spells. It’s an attempt at balance.
Note that, compared to spontaneous classes, the wizard’s access is still superior: a wizard gets to add more spells to their spellbook for free, automatically, than a spontaneous class can learn in a given level.
Disadvantage: major weak point
A wizard is dependent on their spellbook; that makes it a major vulnerability.
How large a disadvantage this is in practice varies widely, though: a spellbook is so core and iconic to a wizard that many DMs avoid taking it away as “un-fun.” A wizard’s complete spellbook is so valuable, and so physically massive, that past editions had rules and lore around keeping backup copies and using smaller traveling spellbooks with fewer spells, as well as fancy magic book covers and the like to protect them. The ideal case, perhaps, is that the wizard puts some effort into these sorts of options in order to protect the spellbook, but those protections are sufficient, so rather than being a binary issue there is a lesser cost associated. Landing on that sweet spot requires a fair amount of same-page-ness between player and DM, but then, so does most of D&D. Note, however, that changes to spell preparation in 5e make a lost spellbook not nearly as crippling for a wizard as it had been in pre-4e editions (the 4e wizard was completely different and not at all comparable to other editions’).
Advantage: Greater ritual access
Unlike clerics and druids, who must prepare a spell in order to cast it as a ritual, a wizard just has to have it in their spellbook. That allows them to save their prepared spells for other things, considerably amplifying the advantages of ritual casting.
Advantage, sorta: Arcane Recovery
The wizard’s Arcane Recovery feature is potent, and requires a spellbook. Again, in the theoretical case of Arcane Recovery being available without a spellbook, that would be better—but again you don’t have that option. It’s kind of hard to really say that this is an advantage to having a spellbook, per se, but it’s definitely part of the overall advantage of being a wizard.