The short answer is no, they will not perform the same.
The beginning of the longer answer is that one isn’t necessarily better than the other overall, but one may be better for your preferences or use case.
Rambly details about why it's preference
ABS and PBT are structurally different types of plastic, and keycaps come in a whole range of thicknesses in both materials - and a few others, too. Blends are also common these days.
When it comes to keycaps, the biggest objective advantage to PBT is that resistance to shine. It also tends to sound and feel different than equivalently shaped ABS, but that’s more subjective. An objective disadvantage to PBT as a material is its tendency to warp when cooling after being molded; you’re more likely to run into twisted or bent keycaps in PBT than in ABS.
Blended PBT sets (including ones whose marketing may not mention they are blended) resist shine better than ABS, but not as well as pure PBT - over time they will shine much like an ABS set. Blends mostly show up in budget doubleshot sets, or in general doubleshot sets that claim to be PBT without much detail given.
Some folks prefer the sound and feel of PBT, some prefer the sound and feel of ABS. For me, it depends on the profile and the other parts they are paired with. For daily use, I tend to prefer PBT because I do have oily skin that quickly shines ABS sets - but I enjoy using those ABS sets more because of the sound and feel in most cases.
“Quality” with keycaps really comes from the care taken in manufacturing and possibly the purity of the material - but thickness on its own isn’t necessarily good or bad. I have some thick keycaps I’d call poor quality because they have crooked letters and warped stems (YMD laser-etched Cherry profile). I likewise have some thin ones I’d call high quality because they are consistent with crisp letters (Signature Plastics double-shot DSA profile).
I think thin keycaps pair well with light or otherwise subtle switches; they let you feel more of a light tactile bump, or experience more of a given plastic’s texture. Likewise I think thick keycaps pair well with heavy or otherwise more intense switches like strong tactiles - and that’s just my preference.
TL;DR: If aesthetic durability / resistance to shine is a key value for your caps, I do suggest sticking with pure PBT. Some of those sets will still show light surface scratches (easier to see on darker colors and fine textures - MT3 Black Speech, for example), but most pure PBT sets I have don’t show any signs of wear at all (any given NK_ Cherry set, for example).