(Bold added in various places to provide a sort of TL;DR "main points" index). There's been a lot of discussion of the differences, and honestly some of the ones I see thrown around are just flat-out false. A common one is that people say that you can't really slur a minor triad into a major in C-griff (and can't go the reverse direction in B-griff), and... neither are true. I generally find it extremely simple to slur a grace-note minor into a major on my C-griff. The diff is that on C-griff you need a spare finger to be available for a minor-to-major slur (not an actual problem in most of the situations I've been in), but can just slide a single finger downward for major-to-minor, and in B-griff it's reversed.
To me, personally (caveat: I have far more experience with C system than with B (which I've only tooled around a bit with)), there is little technical difference to prefer one system over the other (even if you're playing blues and need to grace-note-slur minor and major chords frequently), but I wish I'd been told at the outset that the construction of the accordion, in particular the reed sets available on the instrument, will skew one way or the other depending on which griff you have. In illustration, if you walk into Petosa in the Seattle, WA area and they have new Americana- or Petosa-brand CBAs with four reedsets, the B-griff instruments will be LMMH (and probably dry-tuned), and the C-griff instruments will be LMMM (with one of the M's being decidedly "wet"). But I did not realize this until I was already well on my journey to learning CBA (and accordions in general), and the only real distinguishing factor I had been sold on was that C-griff is gentler on those familiar with piano keyboards, by virtue of the fact that finger movement will somewhat more closely resemble what's used on a piano keyboard (to some degree).
The C system tends to be favored for western European traditions, and so a C-griff accordion is more likely to have two or more mids, and one of those mid-range reed sets will be wet/musette-tuned in order to attain that iconic "musette" sound. If you expect to be playing a lot of Irish, Spanish, Italian, or French folk classics, you may want to learn C system to make more of those sorts of systems available to you. On the other hand, if you wish to play Baroque music (Bach, Scarlatti), and certainly if you're looking for a more eastern Europe sound, you should consider using a B-griff instrument, as bayans, and more generally B-griff accordions, are a bit more likely on the mid-range instruments to have the "high" reed sets (LMH or LMMH vs LMM or LMMM). I'm also not positive, but I have an impression that bayans (which are more commonly available in B griff) are more likely than average to have free bass or converter options.
If I'd known this from the beginning, I'd almost certainly have started my journey on B griff, since I'm very much interested in playing traditional classical (conservatory) music and have been from the beginning, coming from a background in (mainly) classical piano music. Since I have (among other instruments) a Roland V-accordion (the compact FR-1xb), I was able to experiment with B griff (by putting the instrument into that mode), to see if there were any obvious technical advantages to playing that griff over the C - to see if there was a difference great enough that, coupled with my belated understanding that the different systems are associated with different sounds, might convince me to switch systems (I was only 7 or 8 months into playing, but had already made a lot of progress and would have had to reset my knowledge almost completely, aside from Stradella). But I didn't really find grounds to do so (I do think the chromatic scale is a hair more fluid to play in B system, owing to the use of the middle three fingers, rather than 1-2-3 in C system). I also found that, while the sounds definitely skew a particular way, you certainly will find LMMH (and the occasional converter option) for C system instruments, and presumably you can find wet-tuned B griffs (I haven't really looked). It mostly matters because CBAs in general are much harder to find in the USA than PAs, so even a mild skew matters - you're going to be limiting your ability to obtain certain sounds among an already-limited set of instruments.
