I voted in the "try a little of both" camp, although the day you are going and the hours DL is open make a bit of difference.
A lot also depends on your 'to do' list and your touring style. If you just kind of want a good 'highlight tour' of both parks without too much stress or need to get on X number of rides in the day, you can have a very full and rewarding day. If you want to try to cram a lot into the day in both parks, you will need to utilize as many time maximization techniques as you can, meaning possibly Ridemax, Fast Passes, make reservations for any table service place you may decide to eat, get to DL when it opens and stay until when it closes, etc. I always think that getting a sampling of both parks in one day is good - and, in fact, if it happens to be a time when people in DL are packed like sardines, you may welcome the 'escape' over to DCA. That's what lots of people do - they head across the Esplanade to DCA when things get to be too crowded in DL.
Also, because the very popular and entertaining Aladdin show in DCA is ending in August, I would say that, if for no other reason, go into DCA just to see that before it leaves. Plus, the Animation building is quite nice. The Monsters Inc. ride is really cute. California Screamin' is a big favorite for people. And depending on when you go, World of Color may be open. There are lots of cool things to see/do in DCA, but, of course, there is more to focus on in DL.