I am looking for a drilling again.  I am open to the 12 or 16 ga, both have their pluses and minuses.  Causing me to be open to either.
For the rifle I would prefer a 30-06 but I am opened to a rimmed cartridge.  If I go with a  30-06 I dont need to buy any additional ammo.
In my combo guns I shoot mainly non rimmed cartridges with out any issue.
In the drilling is the rimmed superior? 
  IF, i'm spending the $$ to get something like a drilling, i want everything to be as proper and smooth working as can be, and rimmed cartridges just work smoother in a break open gun.  I've owned both, and i kept the rimmed version, that doesn't mean rimles won't work for you though. 
  Same deal with 12 or 16ga.  12ga drilling are "clunky" and not my cup of tea!
  DM