The main reason to split it, as I mentioned before, is if that's only way you have of keeping Hilton HHonors points alive. (Delta miles "never expire", so you shouldn't need the split for that reason with Delta.)

The other reason to split it is if you are aiming for just a particular amount of Delta miles, then when you reach that, you may (or may not) want to start earning something else at that point.

A final reason is if they offer a bonus in one program that you can't get in the other program. Then you might as well use that program just to the degree needed for the bonus, and then go back to your main dining program.

I actually juggle 4 airline dining programs (AA, AS, DL, and UA). In my case, I dine 11 times with each a year (to maintain the top dining program status in each), and then concentrate on whichever one I'm most interested in building up at the time, or if I get a new credit card for one of those airlines then I might use it for that airline until I meet the minimum spend (but then go back to my normal patterns just decribed). I did sign up for one or two hotel dining programs years ago, as well as the Southwest Airlines (WN) dining program, but haven't used any of those in years, the earnings on those are too low (compared to AA, AS, DL and UA) to bother.