Can't comment on the NI library, although I'd love to hear from someone who has experience with it. From what I gather, it's really a different animal entirely from the other two. Not just a percussion library, it also has piano, bass and trumpet. I passed on it because it has no tambourines or egg shakers. 6 guiros, though!
Jamcussion has a wider assortment of instruments than Brio, e.g. multiple shaker and tambourine types. I've never used Jamstix to automate percussion rhythms, and would like to hear from anyone who's done that.
Brio is just a sequencer (actually multiple sequencers, one for each instrument) while Jamstix, of course, actually generates patterns on its own. Brio's pretty easy to program, though, if you've ever used a Kontakt-based sequencer before.
I like Brio, but truthfully, I haven't used it much. But then, I haven't used Jamstix for a while, either. I'm still looking for the ultimate hand percussion instrument. At this point, I don't believe it exists yet.
You might also have a listen to Shimmer 'n Shake from Nine Volt Audio, although it's just shakers and tambourines, no cajon, bongo, conga etc., no built-in sequencer (lots of loops though) and no alternate microphone options. Not really in the same league as JS and Brio, but best in its class AFAIK.