One Bloody Renaissance.
Even two years after the release of the first Assassin's Creed, Ubisoft Montreal remains undisputed in their mastery of traversing through and scaling buildings. More than any other game I can think of, Assassin's Creed II makes climbing ledge-riddled towers, shimmying across rooftops, and skipping from one wooden platform to the other truly feel like second nature. You're not mashing the A button to jump up to the next ledge; simply by holding down the trigger and holding the stick in a direction, your character smoothly transitions from one animation to the next, with few stutters or hard stops. It's both intuitive and genuinely satisfying.
The fluidity of the platforming is compounded by the fact that the environments that you're crawling up are the cities of Florence, Tuscany, and Venice. Each ledge and roof fits into the world, and appears to serve a purpose other than to be scaled. You still get cases where certain bricks will stick out of walls in suspicious patterns, but they're in an extremely small minority.
These two things are the game's greatest asset; not only is the climbing and platforming near-flawless, but open in that your path to and from any mission is your own. However, there are a few key spots in the game (usually in enclosed areas), that force you onto one particular path, and this is altogether less fun. When you have to jump onto one specific platform and then another in order to proceed, the game becomes more like Prince of Persia than it should. It isn't that linearity is bad, but when you're used to choosing how you'll get somewhere, having to figure out the order you have to navigate what is essentially a three-dimensional maze is much less fun by comparison.
Of course, there's much more to the game than its Parkour aspects, and this is where it's able to make the most improvements over its predecessor. In this respect, Assassin's Creed II cleans up as much as it refines. The first Assassin's Creed tackled several concepts and executed about two-thirds of them well, and II cuts out what didn't work, improves what can work, and adds a host of elements that make the overall experience better.
The most noticeable change is the structure of the game, or the lack thereof. You're no longer required to do a set number of side missions in order to advance the main story. Instead, the game encompasses everything that you'll need to know about your assassination targets in the story missions, where before side missions were your method of gathering information.
Because of this, the game feels much more open and varied in nature. Since the side missions reward you with cash that can be used to upgrade armor, weapons, and a villa (a mini-game where you can invest in several parts of a stronghold to increase its value, which in turn gives you more money), you're more inclined to do them because they feel like a reward rather than a punishment (you can also choose to not do them and still end up okay). Because I wasn't forced to do them, it became easier to distract myself with them when I got tired of the main quest.
The number of side missions is also much higher than in the first game, but it's more than a numbers game. The new side missions range from uncovering old tombs to full-on assassinations, with each type of mission having its own self-contained story. This, along with a number of collectibles, extend the length of the game for completists without bothering those who just want to enjoy the story quest.
Another much improved aspect is the dual-storyline approach that the original game took. The story of Desmond Miles and Abstergo takes a much farther back seat than it did the first time, which means less interludes and longer sessions in the Animus, where Desmond relives the memories of new protagonist Ezio Auiditore, who happens to be a much more interesting character than Altair.
Ezio's history is better defined and fleshed-out, his motivations are made clear early on, and his playboy wit is a nice contrast to Altair's cold, uncaring arrogance. You're learning your assassin skills at the same time he is, where before your character already knew everything he was capable of doing, and simply refused to do it until certain points in the game.
The flow of the story is also more interesting. It plays out like an odd combination of The Count of Monte Cristo and The Da Vinci Code. Since Ezio's story of revenge takes precedence to continuing the story from the first game, your main interaction with the world outside renaissance Italy is commentary from characters during your sessions in the Animus, as well as Glyphs that you can find in the world that reveal more about the conspiracy that resulted from the end of the first game. It's a bit detaching to learn about an alternate history of the world in between missions where you're piloting a flying machine into a palace, but it works well enough.
Combat, on the other hand, still manages to be the worst part of the game. It's better than it was in the first game, but it just doesn't match the rest of the game in terms of quality. The theme of diversity carries over into it, with a larger variety of weapons than before, both from Leonardo Da Vinci's workshop and from the ability to steal an enemy's weapon and use it against him, but fighting enemies is either too easy to be interesting or too hard to be worth it. Even with all your new toys, you'll find that you'll still end up resorting the same tactics you did before. You'll either stand still and wait to counter an enemy's attack to kill him instantly, or you mash the X button until you kill an enemy that takes more hits than any human could.
Fortunately, it's no longer your only option. If a group of guards is blocking your way, you can fight them, but it's much more fun (and effective) to hire a group of Courtesans to lure them away, or to hire a group of mercenaries to fight for you. The problem is that later missions have these options less frequently, which means that you'll forced to either sneak by guards unnoticed or face them.
Worse yet, there are a couple of missions that end instantly when you're detected, as well as missions where you have to fight bosses, who are essentially regular people with incredible amounts of health. It's frustrating, but aside from missions where you're forced into combat, you can get by most of the time by assassinating guards without being noticed.
A lack of variety is what made Assassin's Creed, an otherwise fantastic game, into a chore towards the end. Assassin's Creed II, however, addresses that problem, as well as most every other problem that the original had. It's far and away a better game in every respect. Unless you have a preference for the first game's setting, you really don't have much of a reason to play the first game anymore. And for those who didn't play (or like) the first one, you really don't have a reason to not play the second.