I'm your infinity and skylander man

having collections of both.
Both are very different games - the only similarity really is action figures and bases.
Skylanders...
Skylanders fundementally is each separate game (with hidden levels unlocked with adventure set pieces and certain characters).
Skylanders plays like Diablo 3. Each character has a levelling up RPG style chain, and the swappable characters from the new game means that your kids will likely have more interaction and fun with the toys than with Infinity.
During each level you swap in and out your skylander figures, and there is far more physical interactiveness with the action figures. You will be changing up your characters many times during the course of a level, and each level is full of hidden areas, unlocked by certain character elements and combinations.
It's much deeper than it looks on the surface.
Then there are mission challenge maps that are opened up soon into the story which add lots of rewards and replayability, and there is also a fantastic two player battle mode which is like the old powerstone game where you can fight characters against characters. It's good fun and adds to the variety that skylanders had in spades.
As a game in its in right it holds together better than infinity.
Disney Infinity....
Disney infinity on the other hand is completely different style of game.
It's two pieces of a puzzle.
The game playsets are all fundamentally an action platformer where in each world you only play with one or two characters from that universe. You interact in each Playset with only character from that games universe. You can not for example use Jack Sparrow or Mickey Mouse in the Toy Story Playset.
Each Playset plays very similarly with little quests set by npc's and the rewards for completeting them is extra power ups and unlockables that you can take into the 'toy set' part of infinity.
The only playset that changes the action platform thing up is the Cars playset which adds more races to the mix.
Basically each Playset is a separate little game, and lasts for about 5-6 hours.
Once you have played through a Playset you can then go into toy set mode where you can create and build your own little world with unlockables from the Playset.
You can use any character in the toy set mode.
The toy set mode is good fun but the tools are not the most intuitive especially for young ones and I expect they would grow very frustrated with this mode before they had managed to actually build anything good.
Thankfully you can download other users toy sets.
Figures and how you will be playing with them..
The figures are nice but you won't be interacting with them in the same way as they would in skylanders game. You could for example only change use 1 character every 5-6 hours on each playset, whereas on skylanders you will have been swapping and using all your figures.
Overall..
Swapforce is the prettier game too, especially on Wii U. Though Disney Infinity isn't ugly by any means - it just doesn't look quite as good.
Both games are playable on the Wii U gamepad.
...
Personally I like both, but if I could only have one I'd choose Skylanders but either way your kids and yourself are in for a treat.