Years ago I had to buy a new polarizer in a larger size for a new lens I got. I went for the budget offering because "well, aren't they all pretty much the same?"
I was surprised to find my new AF camera was hunting all about for sharp focus. Turned out it was a warp in the filter glass that was causing the havoc (especially since the lens had a rotating front).
It took awhile to get someone at the camera store to believe me - it took a younger guy with sharper eyes to confirm the warp. He quickly recommended upgrading it to one of the better recognized brands - and the problem went away.
Even so, in recent years I've seen really atrocious polarizers (or at least what pretend to be polarizers) bought by those who thought they were getting a bargain on line. I've also seen "infrared" filters that were really just very dark orange glass with no measurable infrared effect at all.
That said, there are some really decent polarizers out there these days. I've tested out Nikon, Marumi, Kenko, Hoya, Athabasca, B+W, Rodenstock and a few others. Thin glass, a mount that won't vignette on your ultra-wide, good coatings, and a nice neutral colour balance are all things you need. Distorted warped glass that skipped through quality control, you can do without.