it'll slow the sub down if its too big i think so it won't react fast enough between bass tones and sound pretty bad, could mess up the sub by over excursion.
It will react quicker with a larger box, you'll lose a little power handling and SPL, but it results in a wider bandwidth and a less boomy response, but that is also largely dependant on the suspension of the subwoofer you're using.
Ya, it depends on the subwoofers suspension and motor. A big box for a Brahma can be a good thing because they can reach maximum excursion with a lower amount of watts in a sealed enclosure. It all depends on the woofer