I'd have to think its the servers as all data is kept on the client side and it's continuously sending information back and forth between the console/pc to the server. It's nothing really to do with the platform you are on. Another issue, that could be related but not entirely, is the amount of data sent and the frequency. During the live letter he mentioned making demi bahamut transparent because he was too big but he said that would create collision errors with other objects and that would stress the servers. If something like a transparency could cause issue I'm likely to believe its on their end and not ours.

On a side note people are really complaining that bahamut summon is too big? Maybe they haven't played through coils and or other FF's but he's always been huge and this is probably the smallest I've seen him. I think it's awesome that he's huge. Feels like an actual summon.