A friend of mine has a Remington 700 in 7mm-08, and it's definitly a nice cartridge. However, I have a few criticisms of it. A) Ammo is about $40 a box for the "cheap" stuff around here, so if your on a budget or can't reload, stay clear. B) If you can't reload, it's nigh impossible to find around here, i.e. you can only get it at one store in a 20 mile radius. C) The 7mm-08, like most of the necked down cartridges, burn through barrels quicker, but that's not a problem if it's only a hunting rifle.
As for the benefits, from what I can remember, it has better ballistics that .243, but they're are still similar, much like the relationship between .270 and .25-06. The smaller bullet is slightly better suited to varmints, but it's not a night and day difference, just slightly.
Either way, your best bet for these is to make sure she's a dead shot. Both of these will bring a deer down, but if you don't hit it right, all your gonna do is wound it, which is pretty cruel. This is the main reason why I think that smaller calibers aren't the best for beginner hunters. But, if your confident in her ability, I'd say it's more of a matter of economics and ease, as she'd be well equipped with either.
Just my $.02, Good Luck!