Well, it depends.

Purely in terms of amenities and in-flight service, DL BizE on a 777 is nicer than Biz on an AA 777. The differences in terms of service are now negligable. However, DL's BizE product on a 777 only has 6 seats accross (2x2x2) versus AA biz class which is 7 seats accross (2x3x2).

The downside is your tickets on DL will also likely be much more expensive than on AA, because only Y/B/M fares are internationally upgradeable on DL. You didn't mention when you were planning on going, or where you were planning on originating, but just to give you some numbers for comparison, here's what the different cheapest fares would be for a few different months, and different cities. (These are the cheapest published base fares that are upgradeable -- no taxes/fees included)

SEPTEMBER..AA Fare.....DL Fare....Difference
JFK........$ 548.......$ 904......$356
ORD........$ 568.......$ 963......$395
SFO........$ 658.......$1126......$468

NOVEMBER...AA Fare.....DL Fare....Difference
JFK........$ 378.......$ 904......$526
ORD........$ 418.......$ 963......$545
SFO........$ 468.......$1126......$658

The reason that DL's fares don't change between seasons is because the upgradeable fare classes are part of the permanent rate structure. So, if you're traveling during a more-peak time, the cost difference will be lower, but will still be significant.

Hope this helps.