Never actually got round to playing the first of these, but I suspect it doesn't significantly impact my enjoyment.
In the first game (as I checked with google), you were a tiny, roughly human-shaped figure, made out of yarn. You worked your way through a series of puzzles and did some platforming, with the assistance of a dangling thread that you could attach to various bits of scenery.
Here, there's two of you. Now, this game can theoretically be played on your own, with you running both of them, but this was picked up as another friendly co-op to play with the Girl, with each of us controlling one. The two creatures can operate independently, each having their own lasso they can use to pull things, climb, and swing from. However, they're also attached to each other by a limited amount of thread, and this is where the complexities (and arguments) start.
Each person can act as an anchor, which allows the other to swing on them. Or you can work together to build bouncy bridges throwing you around the screen. And you might need to have one of you push a handy platform into place to allow the other to ascend to a height, and then climb up to join them. This leads to some tricky puzzling, when you need to work out exactly which order you need to dive over some hook, or tie yourself in knots around a branch. Thus far, it's caused occasional annoyance, but it's reasonably forgiving, so no out and out fights.
Just in case you find the main storyline puzzles a bit simple, or you have a masochistic streak, there are also a range of side challenges which up the difficulty by requiring either quicker movements, better timing, a more twisted logic in the puzzles or just being nearly impossible. To increase the struggles you'll face with all the jumping about, there are also threats that are lethal to small wool creatures, such as fire, water, or turkeys.
One of those hazards in particular, the troublesome fire, makes one of those optional mini missions the most frustrating, as you have to swing franctically around an array of points while dodging a wool-seeking fire missile. That one took me a good five minutes to pass, and nearly broke me. Lovely feeling of satisfaction when I completed it though, which is also well spread throughout the game. This delivers nicely on the "ah ha!" moments when you work out what you're meant to be doing.
It's also completely gorgeous. The graphics are deliciously smooth, and present a world richly full of detail. This applies both to the backgrounds, which contain a wispy story of real people metaphorically(?) following along with your little creatures, and the obstacles you face as well. It has a very crisp feel, and some of the action sequences dash right along.
While it's probably still fun playing it alone, I highly recommend you play it with a pal. The joint working out of puzzles, and the interplay of ideas as you come up with suggestions is great, and even if one of you is worse than the other at jumping or swinging, you can sneakily combine your two creatures together to complete some tasks. It's always entertaining.