Which would you pick for average to large body deer and maybe a few elk?

Either Slayer. I have several mags including two 7mms. But in all honesty I think a .270 WSM loaded with the right bullet is as close to "the perfect" North American round as you are likely to find. I am absolutely smitten with the Kimber Montana in this caliber. It certainly will find its way into my safe, likewise for the Sako FinnLight.

BTW if you just cant decide, Sako is picking up the 7WSM for 05 in their rifles. That way you will have the best of BOTH worlds from the calibers you asked.
RA

For large deer, and because you are including Elk in the bag, I'd go with the 7mm Rem.
Mag. Power wise (velocity/energy) the 270WSM is pretty good, but I'd opt for the 7mm
for the heavier bullets available, both in factory ammo, and as handloading components.

The 7mmremmag because of the wider variety of heavier bullets.

7 mm all the way. It is better suited for larger game and carries heavier bullets.

270 WSM if it is ONLY for whitetails.

I picked up the 270 wsm mainly because I wanted something new and different. I can't see the 7mm remington mag doing anything the 270 wsm will not do. If you are hunting something that requires a bigger bullet you will need something bigger than a 7mm bullet anyway. Availability of ammo and and bullets is greater with the 7mm rem mag though So pick what you want and like.

I’m not sure on the availability of bullet selection for factory shells for the 270wsm but when reloading you have the option of bullets from 90 gr. to 160 gr. With these options you should be able to take care of most size game in North America with less recoil then the 7mm Rem. Mag although I haven’t shot my new 270wsm yet. I’ve been hunting with my 7mm Rem. Mag for years and I’m very anxious and curious to make the comparison.

I would choose the 270 WSM cause I have never had one,as for power wise the 7mm holds the edge cause of heavier bullets.