I can't help but shake the feeling that these two chests are very important. We know that the large chests hold valuable items, which brings me to my next point based on completely random speculation:
Could these two chests hold the 2 new secret weapons for Donald + Goofy?
Think about it - if you were to access this room after defeating the data of Org. XIII, your reward would be Lexaeus' Tomahawk and Vexen's Ice Sheidl (Donald and Goofy's new weapons).
I think you'd get these after defeating Org. XIII data, as it'd be odd to get them before you defeated Lexaeus and Vexen.
Which brings me to my next point; if this is true, could this be the room that leads us to the battle with the AU? This would most likely be the final side quest in the game. And I don't know how else you'd get to that map.
Farfetched, odd, I know. But these chests, being large, must have some importance.
(If you can't see them, look near Goofy's HP bar and the far left middle of the screen.)