I know that Angelo Dundee always requested a big ring for Muhammad Ali. Henry Cooper claimed the one used in their title fight was enormous, the biggest he ever seen. Henry defiantly attributed rng size as a disadvantage. The smallest ring I ever saw Ali fight in was the Chuvalo rematch when as an ex champion he could no longer call the shots in the other mans home town. As it happened, it was a more competative fight, but then even Chuvalo would admit Ali was not the same fighter second time around. The thing is, most gym rings are smaller than competition rings so most fighters have experience of them and can work a small ring if they have to, but clearly the bigger the ring is it is that much harder for a swarming type boxer. When we boxed as amateurs our coach always used to say "don't worry, it's a small ring tonight so it will suit you" or "it's a big ring so finish up on our side and you won't have so far to walk back".
Smallest ring i ever saw for a big heavyweight fight was Gary Mason v Ty Biggs..Albert Hall 1989. Size suited Mason as however much Biggs moved Mason could still reach him..tiny ring for 2 such big guys.
Well, it stands to reason that a large ring benefits guys who like to move and box at range, whereas a small ring benefits guys who like to pressure and fight at close quarters.
Look at floyd mayweather. The rings are big not giant but for a 5'8 guy it might as well be a giant ring for a hw. Its not easy chasing a small guy down in a ring like that. if you are a power puncher or swarmer a small ring is better, mover big ring is better. Come to think of it, judging just by size, jack johnsons ring were enormous but then you couldn't use the ropes to lean on back then so it was different.
Also, it changes the pace of the action. Smaller ring generally means a higher work rate. I know they did some math on that over at fight matrix or some such website and concluded that it also mattered how big the fighters were. A decent sized ring for heavyweights would be enormous for two minimum weight fighters.