sometimes bettas freak out if there's TOO much space..it means that he'll have more "turf" to control...and it may make him stress out. Otherwise, if you have a lot of stuff in there, heavily planted, decorations, etc. He can visually stake out a little territory and you'll see him sleeping in the same place every day...it'll be his "hood". lol
Other people have said they had them in a small 1 gallon, put them in a 10 gallon, their betta freaked out, was depressed (for a long time I might add), etc, then when they put him back in a 1 gallon, they were all active again...so i guess space also depends on the betta's personality.