Jake,
I'll try to help with my opinion anyway.
I don't have the B-1, but I do have the B-3. I don't have the C-1 but I do have the T-3 tube version. In comparing the 2, I would say if you were going to be using them for Vocals mainly, I would use the C-1 (or T-3 in my case). It is hyped a little more in the highs and mid lows to compliment Lead type vocals, it also works very well on solo acoustic guitar.
The B-1 (or B-3 in my case) is more neutral but also seem to pick up the transients a little better. (perhaps it is a function of having a 3 micron diaphram as opposed to the 6 micron in the C-1).
If you are looking for a more neutral mic that works well on instruments and background vocals I'd go for the B-1/B-3.

You may want to wait till you have a chance to try out your new KSM 44 (is that a large diphram mic?)to see which hole you need to fill.

My two cents...

The B3 has much better off-axis response than the B1, which can be important if you will be using it as a room mic.

I've had fantastic results with some female vox using the B1. For the money, B1 is a very good value. Very nice on acoustic steel-string guitars too.

Bowisc