In that particular price range, I'd opt for the B1, but that's based mostly on personal preference, mind you.
I owned the v93 / 2003 for a while, and although I liked it on certain things and for certain purposes, it's not as useful or utilitarian as I would like. For starters, that frequency response curve they publish is way off. My guess is there must be at least a good 4-5 dbs worth of treble boost somewhere in that thing.
It is what it is, though ; a bright mic. On the plus side, it's not exactly bright as in brittle or harsh, like some of it's other budget Chinese and/or Shanghai cousins and siblings. And nothing like the original Rode NT1 or AKG C3000. So I did find it useful in some instances; particularly on dull-sounding instruments and/or voices; like old, crappy guitars or voices who mumbled or didn't annunciate well.
But what really cuts down on it's usefulness is the way it layers. You really can't expect to get a worthwhile recording after layering more than one track using it. Not unless you want your recording to scream "home studio," that is. It has this way of accumulating this yucky high-end stuff, and after repeated listens, you kinda' say to yourself, ears sore and fatigued, "Where the heck is that coming from?"
B1's a different story. It's got a lot of uses, and it does it's job respectfully and without a lot of color or fanfare.