Hi Kanal,
You are right, they are are not the same. The reason they are not the
same practically is that the noise covariance when generated after
bandpass filtering the signal first can be very very different (in
scale and possibly also in the spatial structure) and hence the inverse
operator is different.
I would vouch for computing one inverse operator with the entire band of
interest (0-100Hz for example) and then looking at narrower bands once the
data is in source space. My reason for that would be to not impose too
much temporal correlation in the noise by band-pass filtering in sensor
space. MNE as such is equivalent to a maximum aposteriori probability
(MAP) estimate of the source space activity only under the assumption that
the noise is uncorrelated in time. It is robust to violations of the
assumption to a large extent (correct me if I'm wrong here) but filtering
around 7Hz, for instance to look at alpha makes the noise heavily
different from its assumed no temporal correlation behaviour.
Having said that, if its an event related paradigm and you have enough
trials and excellent SNR, doing it either way should not make a
difference.
Regards,
Hari