The decision
People get weird about cookware. Somewhere along the way we decided a serious kitchen needed a matching 12-piece set from one expensive brand. I don't buy that. I'd rather have a few really useful pans and spend differently depending on the job.
A 12-inch stainless fry pan is one of those useful pans. It can sear a steak, brown chicken, build a pan sauce, sauté vegetables and go from stovetop to oven. Unlike nonstick, you're not buying it with an expiration date in the back of your mind.
Stainless is also a category where I can justify paying more — but I don't think you have to. All-Clad is the nicer object. Tramontina gets remarkably close for much less.
What I notice
The reason I like All-Clad isn't that it performs some magic trick the Tramontina can't. It's that everything feels resolved: the construction, the responsiveness, the durability, the confidence that you're buying a pan you'll still be using years from now.
But here's the problem for All-Clad: Tramontina is really good. Once food is in the pan and dinner is underway, the gap feels a lot smaller than the price gap. That's exactly what I mean by 90% as good for less.

All-Clad D3 12"
Excellent heat control, proven construction and the pan I would choose if I were building a kitchen for the long haul.
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Tramontina Tri-Ply 12"
The rational choice. It gives you most of what makes good tri-ply stainless useful without paying the All-Clad premium.
CHECK AMAZONDon't buy the set
If you're building a kitchen, I wouldn't automatically buy either brand's giant cookware set. Buy the pieces you actually use. A great fry pan, a good saucepan, a Dutch oven, cast iron — build around jobs, not matching logos.
The one I'd buy
All-Clad — but Tramontina is the recommendation I'd make without hesitation to someone who wants to save.
If the extra money won't bother you, the All-Clad is the one I'd want to own. If you're staring at the two prices wondering whether you're making a mistake buying Tramontina: you're not.