I just got an AX5B last week cuz I ahd extra money on a gift card and it was cheap. I also previously used a Zoom B2 so I can give some helpful insight.
Zoom B2 - Great for modeling. Was able to get a really good sound out of it to record into a not so great amp. Really warm and clear. Effects weren't anything to write home about. Compressor was so so. Kinof a pain in the ass to program, B21.U would be better just for the sake of USB programmability.
Korg AX5B - Just got it for $40. Easier to program, but you defenitely still need to sit down with it and program some stuff out. Models actually sound decent, I've got better equipment now so I don't use them. Effects are pretty good on this unit. Synths, Ring Mod, Pitch Shift, defretter, slow attack etc... All pretty good. Delay's, echo's and chorus's are all good. Can control level of everything and blend of almost everything. Expression pedal is amazing. Has clones of many saught after efffects, RAT, White Crybaby, Muffs....The BAD news, defenitely colors tone. Got it just before recording this week, so i threw it in my chain just to try it out. having it bypassed in the signal chain will alter your tone abit. Enough that I wouldn't be able to leave it in.
I plan on getting a LS-2 so I can have some effects out of my signal chain. Fun to have, more fun than the B2, just depends if you want modeling, or effects.
Forgot to add. The Korg AX5B has a dedicated synth processor. These are some pretty damn good synths.