Hi Will,
I have 1 piece of both (B87A and B87C) and as already referred they have a bit different "flavour".
When you are using B87, you typically have that miss or hit situation. Why? _I've_ found that with B87 you easily miss the benefits if you are having a "basic sounding vocalist". It might be actually that it enhances some of the frequencies you might not like in his/her sound.
Where I've found B87 working with "hit" is when I have had a vocalist that has a personal, strong sound. Then B87 just give you the extra to make the sound really flying IMHO.
What comes to C or A, depends from various things.
If I am doing the FOH and I have someone else doing the monitors and the singer knows what he (typically B87 is used for male voices and 86 for female if you use Shure...) is doing I like to go to the A-model because it picks up much less ambient sound (IMO).
If I am making also monitors myself (especially IEM), or I have a bit uncertain singer, I would use the C-model, because it is not THAT picky about the singer's position behind the mic. For the monitor's it makes the sound a bit "rounder", because it is picking other stuff (reverbs etc.) a bit more.
What comes to other possible mics, I could recommend to look also Sennheiser products. I've found e935 and e945 to be quite nice ones. The difference between Sennheiser models and Shure B87 is that with special sounds Sennheiser is not THAT special (but still good) and with "normal" sounds I found it even better than Shure B87.
But as a bottom line, it all depends on your own desires and taste.
To be honest, if someone is having a comment on either "A" or "C", he/she most likely brings an own mic, or it does not even matter which polarity you have... ...IMHO...
Br,
-Minka-