This is false and I have proof.
The Retro Series Review - the HD 7870 versus the GTX 680 compared with the RX 570 and the GTX 1050 Ti benchmarking 38 games
babeltechreviews.com
Please I implore you to read this whole article. Really pay attention to the summary and the tests at max settings but the
Real Bottom Line: is that more vram 100% can contribute to the performance of a GPU. Back then a 50% increase in memory was a big selling point and while the 680 handily beat the 7970 at lower resolutions, it really fell behind at higher res. And now here in the future the 7970 absolutely eclipses the 680 and can handle high texture settings much much better.
One could argue something along the lines of AMD fine wine or nvidia gimping drivers/not adding new support. And maybe thats part of it, but seeing this massive divergence in performance historically, why would you want to artificially limit how "future proof" your gpu is? Especially considering consoles are easily going to be using 12gb+ of vram in a few years easy.