I have Infinity as well as all of the Skylanders games, as my daughter and I enjoy playing video games together. Since everyone tends to assume that Infinity is "Disney's Skylanders rip-off" I'll comment on both.
The concept of the Skylanders games doesn't change much from game to game, but that's fine because it's a fun concept that is well-executed. The individual levels will probably each take you an hour or more to complete the first time through, and there's plenty of replay value in looking for hidden collectibles and even leveling characters. They basically add a minor tweak with each new game:
Skylanders: Giants - Skylanders with larger figures that can smash barriers in the game that regular figures can't
Skylanders: Swap Force - Skylanders with figures that can be pulled apart and their tops and bottoms combined into new "characters."
Skylanders: Trap Team (not out yet) - Skylanders with "traps" (physical toys like the characters but a different shape) that can be used to "capture" a villain in the game so you can play as that villain.
Disney Infinity is... not Skylanders. The similarity frankly begins and ends with the fact that both of them have a USB dock that reads RFID chips in the toys. The Disney game (based on what I've seen, we've played it some but not a HUGE amount) has two game modes: A series of "games" that are each based on a particular Disney "world" (i.e. Cars, Monsters University, etc.) and an open-world game called the Toy Box.
The Toy Box could loosely be compared to Minecraft with Disney stuff. As you play the other games you unlock models for characters, vehicles, buildings, etc. that can be thrown together however you like in the Toy Box. You can then run around in the world you've created.
As far as the other series of games go, I've played several of them. They're similar to a LOT of other games in that they have multiple "levels" that you can move between, various types of collectibles, a somewhat open-world approach to missions ala an Elder Scrolls game, etc. But they're like miniature versions of those games in that they're not as long as a standalone game. That's offset somewhat by the fact that there are a number of these games built into Infinity, but keep in mind that these "large mini-games" (for lack of a better term) are unlocked via physical game pieces and only one is included with the game, so they have the same business model as DLC.
The other thing is that (IMHO) they're... not very good. Don't get me wrong, they're OK, and kids might have fun playing them, but the plotlines, the missions, heck even the controls at times are not as good as a top-quality title like Skylanders or a first-party Nintendo game for example. After getting somewhat bored with it, my daughter and I gave it a second try recently by trying out the Cars "game." I played it for an hour or so but eventually grew frustrated by poor driving controls. Considering that driving controls are the core movement mechanic in that game (because you're a CAR) that's kind of a big deal.
I will say that some of the games are better than others. The "Incredibles" one was notably better than the others I played. But since you have to pay for them, it's probably best to do your research before purchasing a set that includes a new "world game" just like you would read reviews before shelling out money on a standalone title.
If you think you'd enjoy the open world stuff then you could perhaps start with the starter set alone and try it out. But if I was a betting man I think you'd have more fun with Skylanders.