I don't think the British vehicles (FV432 and Warrior) have significantly smaller doorways that M113s and Bradleys, it's just that the back is vertical wit ha single swing door, rather than sloping with a ramp.
There are a couple of disadvantages to the ramp:
1. It doesn't work if the vehicle power is off. Yes, they have emergency swing doors set in the ramp, but they're much smaller.
2. It can have problems if the ground behind the vehicle isn't flat: what if the end of the ramp comes down on a big rock, or a piece of urban street furniture?
On the other hand, there are a couple of disadvantages to the swing door:
1. If the hinge is on the left, then the door is hard to open when the vehicle's on a cross-slope with the left side higher, because you have to lift the weight of the door against gravity. Vice versa if the hinge is on the right.
2. Likewise, if the vehicle is on a right-side-higher cross slope, then a left-hinged door is hard to close, because you've got to lift it against gravity, and vice-versa.