I have both and have killed quite a few critters with both. As some have noted, one CAN kill an elk with a .243, but we're talking under ideal conditions--most likely a broadside shot on a stationary animal while using the proper bullet for the job, at a reasonable range.
The 7mm-08 is more ideally suited for this task, and I feel more comfortable with 7mm-08 on "less-than-ideal" shots, especially with all copper or non-lead bullets, like Hornady's GMX bullet or Winchesters 95/5 bullet (which I suspect is just Hornady's GMX bullet under another name).
However, since you said this rifle would be for your daughter's first deer, I'd go with a the smaller of the two calibers. The .243 has less recoil, which will allow your daughter to have longer range sessions, reduces the chances of your daughter developing a flinch, and gives you the opportunity to use her rifle during the off season for coyotes. Seeing that your in Pennsylvania, and--I'm making a dangerous assumption here--you'll probably be hunting from tree stands and/or blinds, the .243 will work just fine for the ranges you and your daughter will be shooting.
good luck on your purchase and be sure to give us a report on your new rifle.