Signal processing is much more involved then a digital volume control and bit depth definitely plays a role in the results. Theoretical differences versus what the listener practically hears is a topic of long standing debate.
Check out:
Second-Order Digital Filters Done Right
Using digital input to a DSP based crossover definitely eliminates the extra A/D->D/A. In the case of the MiniDSP and my experience with Analog Devices BlackFin DSP, the results just do not sound as good to my ears as a well implemented analog crossover. I'm not sure what to attribute that to, maybe it has to do with IIR phase characteristics. FIR would be better but the delay may not be OK depending on the number of taps needed. Digital is a funny thing, I can clearly notice a difference between different input types on the same ESS9018 based DAC.
Maybe a DCX2496 would change my mind?