I don't think having a big map makes too much difference, fights will tend to develop and attract those as wish to fight into clumping into big furballs at a base or two, and that's fine by me.
It's a big difference. With a large map, the action is low key and very unstable. You will see single cons all over the map. Despite being looking for action and fun, most players try their luck elsewhere when things are not completely going their way. There are a lot of sneak and early aborted capture attempts. Only rarely there will be a big rad and green darbar. 10 players will attack 10 different places.
I did leave AH last summer because of that, because I wasn't looking for hunting single cons all over the map. The new, single small map offpeak arena made a huge difference. There is definite an unhealthy lower limit for player density. Consider that off peak hours hardly break 150 players these days, and for 5-6 hours the population is significantly below 100.
Why would the map have to be closed to open a second arena back up on peak hours?
Because that's what we had, and it didn't work at all. see HT's comment.