The 737 is much more of a pilot's airplane. You can grab it by the scruff of the neck and make it do what you want it to do. The -900's are more challenging to land well than the Airbus. The Vertical Situation Display and the avionics package allow the 737 to be easily flown with a great deal of precision with regard to energy management. The 737 climbs a bit better.
The Airbus is more comfortable, but about as fun to operate as your washing machine or microwave at home. MHO it is harder to learn but a whole lot easier to operate day in and day out. The Airbus tends to make you look good on landing, so there is that. Took me ~300 hours to learn to trick the FMGCS into flying smoothly. The 320's in particular will do dorky stuff like get ten knots slow, then firewall the power. After a brief while, you'll learn to see the set up and help the airplane out.
The 737 does more island and central America flying, it that's your thing; cheap shoe shines, good empanadas and free boat drinks. The Airbus seems to only go to places where there are a lot of BBQ joints Chick-Fil-A's, Dunkin Doughnuts and $30-$40 hotel meals.
The Airbus has two jumpseats. Jumpseaters and especially the FAA seem to know this and look for Airbus flights. Expect JS about 30 to 50% of the time. The 737's don't go anywhere that anyone much wants to JS to (can't internationally) and they do more red eyes.
The Airbus 319 is the most expensive airplane at Delta on a CASM basis. For that reason, it would not surprise me to see them get culled. The A320's that were the NWA launch birds are seriously old. Expect to become very familiar with the MEL / CDL. Getting them to wake up in the morning, in the cold, takes patience. Make sure your Capt has his cell phone charged, he's going to need it. The passengers love the Airbus (for the most part). More comfortable for them.
ATL is stagnant on the bus. Everybody I speak with is moving backwards due to the MD88 exodus. If you are a west coast bubba the world is your oyst'ah for now.
Nobody seems to know how they will deploy the NEO's yet. Given all the problems Pratt is having with that engine I'm still not quite believing we are going to use them trans-oceanic. After my career, I'll believe it when it's on the gate with my name on the release.