Well, Jasmine had a plan - a ridiculously convoluted one, apparently- that she puts into action and actually succeeds with for some time. The First ... I don't even know. First it has Spike killing people, under mind control, but then randomly decides not to use him yet, and instead ask the non- superpowerful, mostly untrusted Andrew to kill some Potentials for it? I know it was a question of actors appearing, but the fact that we never see Tara or Jenny appear to Willow and Giles, or Joyce appear more than she did, also kind of lessens the emotional impact of The First. Whilst the last battle with the First is pretty epic, it doesn't really feel like it was potentially world ending- we know that Angel will be setting up a second front in LA, and as others have mentioned on these boards before, the Initiative/ whatever it is that Riley is now involved with could get called in, it's pretty much all a question of firepower. With Jasmine, it's quite conceivable that the world might just let her take over- firepower wouldn't matter because no-one would be opposing her.
Jasmine can also touch (and therefore kill) people where the First can't. You could argue over whether this is an advantage or not, though. Jasmine could also be killed, by someone with sufficient power and strength, whereas whilst the army of the First is defeated, it's still "alive", it's not something that Buffy can just defeat.
Overall I went for Jasmine. Theoretically, the First could have been really threatening, but never quite lives up to the promise. I think Jasmine came closer to "taking over the world", if you like.