Is there an advantage to process EEG data as analog (vs digitized) signals?
You MUST do analog processing to make the signal suitable for sampling by an ADC. Do the math. What happens when you have a 12 bit ADC covering 3 volts? Is there sufficient resolution to handle 0.1 mv signals? –  No. The LSB in such a case is about 0.7mV.  At 16 bits, your signal would span a bit more than 2 LSBs.  There must be some amplification, probably by a factor of about 500, to give you enough LSB's to sample effectively, and you need to condition the signal to remove offsets to be able to get a gain that high.

So, attempting to sample without analog preconditioning is probably misguided here.

There is some argument to be made that sampling unconditioned with 24-bit or higher ADC's is OK, but I think that an instrumentation amplifier input stage with modest gain, which is well optimized for high common mode rejection ratio, is a fine thing.