Of the two given rounds, I would go for the 7mm rem mag for a number of reasons.

1. You are already familiar with a shotgun's recoil, which will be less in the 7mag.

2. The 7mag is a very significant step up. With 150gr powerpoints, it will darn near rip a deer's shoulder clean off (if hit there obvouisly)when you go to process it. My point being: if you need for a deer to fall down straight in it's tracks to avoid a creek or a fence, it is fully capable of the job. If that's overkill to you, then there are plenty of tougher bullets on the market including just stepping up to the 175gr powerpoints which are pretty easy to find.
And if you ever wanted to go out hunting for some of the larger animals like elk, you are going to want the 7mag over a 7-08.

3.Remington makes Managed Recoil ammo for the 7mag, which means you essentially have a 7-08 if you want it.

I'd just keep shooting the slugs though