An auto tag heuer and an omega perform pretty much the same, but Omega makes a lot of their own movements in house and. As far as I know Tag does not, and if they do it's only on a select few. All things being equal, I'd rather have the in house movement. That's my opinion, but one could argue that it's more practical to have a VJ7750, etc. than a proprietary movement because it can be fixed locally relatively easily and probably cheaper as well. That's a valid argument, and one reason that I stay away from modern Panerai. Their after sales support is doing them no favors.
Tag also seems to take a bigger hit on the second hand market if you decide to sell it or flip it for something else. Omega is known as a power player in the watch world for generations while, outside of Motorsport, Tag is more of a trendy brand.
If you buy at the right price, and avoid precious metal, you'll probably do fine either way. Though, as noted above, in terms of retained value, Patek and Rolex rule the second hand market.
That said, when I head to Monaco for the Grand Prix, while a Rolex Daytona is a fine choice, but I'll be sporting a Monza. That's a true drivers watch, though a Speedmaster would be a good choice as well.
In the final analysis, it's just man jewelry. Get what you like and don't worry much about resale, unless you know that you're a flipper. I know a bunch of attending level specialists that still have their Tag or other entry level Swiss auto from ~20 years ago.
My father's been wearing the same gold Omega, for 65 years! Take care of them and they'll last generations.
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Il Destriero