Smaller pickups sense the strings over a smaller area so it definitely has an effect - from my experience it makes for a tighter bass response, more highs. Lots of things have an effect on the pickup sound though - pickup width & height, number of turns of wire (more turns equals more DC resistance), wire thickness (thinner wire equals more DC resistance), magnet type & strength, baseplate materials, cover materials etc.
From what I understand both the HB-1 & minihum have a DC resistance of about 6.8K to 7.0k. Doesn't mean that they sound the same though. I'm guessing but maybe the mini-hum has thinner wire & less turns giving approximately the same DC resistance. The best measurable indicator/specification of how a pickup sounds to me is it's inductance (which is a function of magnet strength & number of turns of wire). The lower the inductance, the higher the resonant peak of the pickup & the brighter it sounds. HB-1s measure about 4 Henries - most PAF style 'buckers are 5 Henries or more. A typical strat PU is about 2.7 or so. From those figures you can guess why the HB-1 is renowned for it's clarity, at least as far as big profile humbuckers are concerned.
I won't be getting my minihum equipped guitar for a while but I will be very interested as to what the pickups sound like & what they spec out to.