What kind of power differences are you dealing with here? For example, if you went with 1000 watts RMS of class D (or AB) power to 300 watts RMS of class AB (or D) power, I would think that the lack of output would be noticeable.
there should be no noticeable difference in "bass" when comparing the same wattage in a class a/b to a class d. It's must be the power difference and cabin gain your noticing.