They're nearly the same so it's really pretty negligible. At different points they put a little more stress here and there like on the biceps or lats or chest. I would suggest working both (although I haven't taken my own advice, lol) as muscularly even though they are similar you can get vastly better at one than the other because of constant repetition ingrains it neurologically (similar to GTG).
As for muscles: forearms (there's tons), biceps, lats, chest, posterior delt, teres major, serratus (both). The major ones are really only biceps and lats and possibly teres major and chest. If you have a problem holding onto a bar/wall then probably forearms too.
The funny thing is rows are nearly similar to pullups as well and work pretty much the same muscles except rows add a bit more traps, posterior delts, teres major, and the external rotators while reducing the tension on the lats.
I wouldn't divide the movement up into sections either as you should be pulling with both. The elbow angle closes pretty much in sync with the shoulder angle so the pull decreases and increases about the same on both muscle groups at the same time. The general rule is that the longer a muscle is, the weaker it is though so when you're at a dead hang you're usually weaker than at 45 degrees which is weaker than 90 degrees etc.