Im about to have the opportunity to hunt red stag and eland. The largest caliber I currently have is a 450. Would you feel comfortable on a spot and stalk inside 200 yards with this caliber? My other option is 7-08 loaded with JGs 162 at 2500 muzzle velocity.

Have you practiced taking it out to farther ranges? The caliber can do it, but the trajectory is about like a well thrown baseball.

I have a .458 SOCOM that is a ton of fun, but it's a <150 yard hog gun.

The red stag can be taken with your 7-08 with good bullets (e.g., Partitions, GMX, 'TSX', AccuBonds). Use that if you have one.

The eland is much bigger, much tougher, and more wary. If your shots are 'expected' to be inside 200yds. you'd better know your .450BM's trajectory to 250yds., and DON'T use a pistol bullet (e.g., XTP).

If you see game at 200yds, are you confident the bullet is gonna make it there and do what it needs to? Id take pop shots at a hog at that distance but as mentioned, 450BM is just that when it comes to distance beyond 100yds…..a big BM. Use your 7mm-08

I need to write this essay. For hunting rifles, most people need a small, a medium, and a large. Your 7mm-08 is a medium. For red stag and nilgai you need a large. Something long action magnum. I've got a few options already in hand. Some are fast, some would take months to get complete. Holler if you want to get going on a long magnum.

Forget the 450. You need something equivalent to a 300 Win Mag. A 30-06 at minimum.

Inside 100 yards prolly be just fine, but personally I’d probably go with 30.06 or 300wm, 300prc.
There is no replacement for displacement, and that 450 is gonna run out of steam fast past 100 yards, if you got the dope for it and a dialable scope id say go for it but its nice to have a 200 yard zero with a 300 win mag and dead hold stuff out to about 350

If the shot is guaranteed to be 150 yards or less it does not matter which one you choose. But, IMO, the one that will work well under the broadest variety of conditions will be the 7mm 08. I am old school partial to Nosler Partitions but there are a lot of premium bullets out there. The better a shot you are the better the hunt will turn out.