From a U.S.A. starting point, a Cozumel vs. a Red Sea trip with a budget/value perspective? That's a pretty apples-to-oranges destination face off. I've been to Cozumel; from what I've read of the Red Sea diving, it's on the other side of the world, best done via live-aboard, and the diving is likely better than the Caribbean but not on par with some Indonesian sites like Raja Ampat...but you have the option for land tours like seeing the pyramids, if you extend your stay and topside excursions are of interest.
If that's all accurate, here's the mindset I'd approach your comparison with:
1.) I find air travel rather brutal where long flights are concerned. Even if airfare were similar, for one trip to trap me on more flights for a lot more hours would be an example of 'not equal; nowhere close.'
2.) If I did a far distant live-aboard trip, I'd want to arrive a day early to make sure I didn't literally miss the boat. No need for land-based op.s in Cozumel. Travel to/from the Red Sea I'd think would take 2 days, maybe 3...after all, do you want to show up strung out from jet lag and poor sleep on flights to leap right into an 'I'm doing all the dives to get my money's worth' live-aboard trip? Factor in the added costs of airport food and overnight hotels going and coming for what will likely be 2 extra days going (to get there a day early) and 1 extra coming back. For me, $14/day at Nashville airport's parking lot is also a factor - $42.
3.) Cozumel has good Caribbean diving, but it's my understanding the Red Sea is thought to be better? And there's not going to be a
Thistlegorm or likely oceanic white-tip sharks in Coz. Just comparing potential trip dive counts doesn't tell the full story.
4.) A solid dive trip can be packed into 7 or 8 days in a Cozumel trip (Tres Pelicanos & Casa Mexicana, Cozumel Sept. 2018 Report -
Tres Pelicanos/Casa Mexican Trip Report Sept. 2018 - I got 26 dives in an 8-day trip, no shore diving); for a Red Sea trip, I'd want a 10-day live-aboard to justify all the time and bother to get there and back, and round trip travel time would turn it into a 2-week+ trip. That's without any side-trips to look at pyramids, etc...
I like to apply reductionistic thinking to break it down to total trip cost divided by total # of dives as a value metric, but that's just not adequate here.
If I were comparing these, I'd probably lean toward Cozumel for a simple budget trip for now, and delay your return to the Red Sea until you have a stronger sense of what you want to do when you get there.
Just my 2 cents, and as I said, I haven't been to the Red Sea. Wherever you go, I hope you'll post a trip report about your experience to help the next guy researching. Good diving whatever you decide.