Though at first the difference may seem clear-cut, the advantages and disadvantages create some debate as to which one is "better". miniGOINGS has it all correct, but I'll expand on it with some opinions.
ZZ is done first and intuitively, meaning it takes up your inspection time, making the cross slightly more difficult. ZZ RESTRICTS YOUR SOLVES TO <R,L,U,D,F2,B2>. While it might seem nice, many F2L shortcuts that you learn require some F and B moves. Some cases turn into really strange ones and others are the same. I find, as a casual ZZ user, that there are many more U2s in ZZF2L. Thus, F2L takes slightly longer in ZZ than in pure Fridrich until you adjust. I cannot say what it is like after the adjustment because I haven't gotten there yet. But remember that you have a step before your cross in ZZ.
ZBF2L is quite different. I use an extended version of VHF2L (the 32 + 4 cases that suck otherwise), so I'll use that for my comparison. Your F2L stays the same right up until the insertion. I prepare the edge-corner pair for insertion, then perform my algorithm. For ZBF2L you just take the last pair before this preparation. While it may seem like a lot of algs, many are intuitive. I think I learned 8 algs for my extended VHF2L and then 60 or so tricks to generate those algs. However, while this is a fast step (usually faster than Last Slot + OLL), it is certainly slower than pure Fridrich F2L.
The only reason to use ZZ or ZBF2L over pure Fridrich is if you want to learn a more advanced LL technique. COLL + EPLL is great and, for me at least, is slightly faster than vanilla Fridrich. ZBLL is great but time consuming (I learn a COLL set, forget it, and repeat ever 2 weeks). I like ZZ for learning about the mechanics of the cube and for FMC (mostly just good to know when your edges are oriented). ZBF2L just sounds like it isn't worth it. Intuitively preparing my last F2L pair is just so fast I don't see a reason to learn 240 more algs. I even argue that the VHF2L I know means I know ZBF2L, but I'll save that argument for another day. Hope I helped!