Either is fine. I'd opt for the .06 with a 150 grain standard pill, or a 140 grain in your 7 Mag. I'd get close, so the 24" barrel in your mag might get in the way if you're stalking.
I gave my reasons for this in the post above, but it bears repeating

pardon the pun.
After killing 50+ blacks and a couple of grizz in my career, I advise getting as close as possible and using a bullet with medium sectional density rather than a heavier for caliber bullet on blacks. They are not particularly heavily boned, and do not need premium bullets or heavy ones, either. If you opt for a heavier bullet, use a roundnose. They open up much faster. If occupied, bears are very easy to stalk.
My own choice of bear guns is an .06 (odd, because it is not my favorite caliber, but I think it the best for bears) with a 150 grain Sierra flatbase. I've taken over 20 with this combo, and never more than one shot, and never farther away than 50 yards.
Grizz are a different kettle of fish. Big bullets, and break the shoulder first, if you have a choice. I prefer the .338 or .375 Holland for carrying in grizzly terrain.