Well, you’ve gotten a lot of bad advice here. Although I’ve no experience with either cartridge, the answer to your question is obvious in the title of the thread: TEXAS! Go big or go home! .280 is bigger.
Ain’t bigger. Faster, but not bigger. And faster don’t mean diddly inside of 400 yards.
To the OP: I’ve killed deer with my 7mm-08 out to 541 yards, and elk to 346 yards. My nephew killed his first bull last year, a 5x6, at a bit over 400. You’ll have plenty of gun with the 7mm-08, and it won’t bang you around.
P