What it boils down to is that the Assassin's Creed series is a lot like the Star Trek movies.
For some reason, the Star Trek movies follow a pattern - the even entries are generally way better than the odd ones. There's even a trope about this phenomenon.
I contend that AC2 and AC4 are the better entries in the Assassin's Creed series. The other "Ezio trilogy" entries are kind of so-so and feel very iterative rather than fresh. The less said about AC3, the better. (Although I have met people who like it, despite my protestations...)
This uneven quality level is hard to explain in the context of Star Trek movies, but it's somewhat easier to explain in game franchises. These games build off of each other. Sometimes, due to time or other constraints, a game ends up being more iterative, or so many new featured are added that less time is spent bugfixing and integrating the game as a whole. This leads to either stale games (in the case of Brotherhood and Revelations) or broken messes (in the case of Assassin's Creed 3 and Unity).
When Assassin's Creed is done right, though, the results are nothing short of spectacular. AC3 introduced a ton of new ideas - running through wilderness areas on treetops, hunting, naval engagements and combat - along with a few new weapons and moves like the rope dart.
However, the game is just a mess of disjointed systems that don't fit well together and are annoying to use. A former Ubisoft employee lamented this fact over on Reddit, which is an interesting read if you've got the time.
Assassin's Creed 4, though, takes all of these messy, experimental elements and builds them into a game that feels like it is one, singular, cohesive whole. Tree running was an irritating necessity in the wintery east coast, where trying to run along the ground left you mired in snow. In the tropics, though, it's a good way to get the drop on opponents while you're out and about.
While I'm on the subject of the tropical island setting:
636 pixels of width doesn't do this game justice. It is un-freaking-believably beautiful.
The naval combat was always the strong point of AC3, and AC4 takes the core concepts, polishes it extensively, and then makes it a core feature of the game. As a big Sid Meier's Pirates! fan, I thoroughly enjoy these segments, and they break up the land-based missions well.
The land missions basically boil down to the same Assassin's Creed type stuff we've been doing for years now. They're competently executed and all, but the core mechanics are kind of long past their freshness date at this point. It's never really explained how Kenway is capable of feats that take other assassins years to perfect without any sort of practice or training, but whatever - it's a video game. It's probably "racial memory" or some other pseudoscientific BS.
Speaking of BS, the "modern day" segments have taken a drastic change from previous entries as well. I personally could not stand the modern plotline of the game prior to AC4. It's still not terribly engaging, but at least it's easy to ignore.
There are a number of useful conveniences - fast travel, for instance, is quite useful with plentiful fast travel destinations that cut down on a lot of Wind Waker-esque naval backtracking. The ship's captain's cabin is also a shortcut to doing a lot of things that would normally take you into town - it functions as something of a floating shop, open 24/7 for all your piracy needs.
I do wish we could do without the ubiquitous hunting and skinning minigames in Ubisoft games. I could kind of see it in AC3 where it was part of Connor's racial identity, and he was at least reverent about it. Between the Far Cry series and the AC series, I think I've seen enough skinned animal carcasses in my video games now, though, thank-you-very-much.
AC4 is, overall, a spectacularly fun game. It is the culmination and refinement of dozens of complicated systems that interlock to form a game that is fun to play (almost) no matter what you decide to do in it. The next time it goes on sale low enough to afford, take that leap of faith and jump in without hesitation.
(Cult of the Fiver is my monthly series on great games that can be had for cheap. Want to stay on top of all our recommendations? We have a Steam Curation Page! In Pre-Cult articles, I collect my thoughts about a game I plan to feature in this month's entry.)