the b on my classical is the only string that ever goes out of tune. and it's as predictable as a clock. (which seems to indicate that the tuner is bad.) but i understand it and know the prob like the back of my hand, so it's no biggie for me. (kind of went off on a tangent, but the mere mention of the b string, and i reach for the tuner...)
are we talking about fresh strings here? that might cause some probs.
otherwise, since this problem appears to be consistent for you playing over several guitars, "the problem is you" (great, now i've got the sex pistols in my head...)
lol, at least it may be you... you may be pressing harder/lighter when you play a chord compared to when you are just fretting individual strings... try varying your pressure and see if things change. this can be really noticeable with lighter strings and giganto frets or scallops.... mmmmm scallops.
aside from that, it's the usual suspects. just follow the string from one end to the other: tuners (bad tuners), nut (bad locking nut), frets/neck (would have to be something really weird and obvious), bridge (intonation, trem problems, or even crappy strings that are slipping on the ball end).
(this shouldn't have any thing to do with your amp or cables or anything like that. just turn off all of your effects and run it plain)