In my opinion it would entirely depend on the power supplies in the amplifiers in question. When comparing an smaller amp to a larger amp, the large amp will typically have a lot more brute power and it will make the bass/midbass sound a bit heftier/thicker.
If you are trying to bi-amp with a multi-channel amp that uses a shared power supply, the results are probably not going to be earth shattering (since the different channels will drag down the same shared power supply). In your case, the Parasound A51 has a shared transformer, but completely independent power supply / capacitor banks for each channel. In this case, you will probably get better results with bi-amping versus single-amping if you are just using your A51. However, you may get better overall results by just replacing the A51 with some big monoblocks (like the JC1). Monoblocks will have very large power supplies and may also be fully differential (as opposed to single ended). This will control the speaker movement much better. Also, the B&W speakers really need a high-power high-current amp to sing.