It's mostly cost and finish and a small weight difference. I believe the functionality is nearly identical. The warranty on Dura Ace is longer if that's a consideration. So is the snob appeal. It's your money so you have to decide.
One mechanical difference is that the Dura Ace 10-speed hubs are strictly 10-speed. Nothing else will fit. Ultegra 10-speed hubs will accept 9 and 8-speed cassettes also.
If it were someone else's money, I'd go for Dura Ace. For my own money it's Ultegra.
I recall reading a similar question on the difference between Record and Chorus on a Campy site. The moderator's take was; "Record is 'Pretentious Man's' Chorus." I think this is a similar choice.