Does a larger desk mat or mousepad prevent curling better?

No. A bigger surface doesn’t fix curling — material and construction do. Curling comes from the base layer reacting to heat and humidity, and a thin rubber base on a large mat curls worse due to more leverage. What matters is thickness (~3-5mm rubber), stitched edges, and flat storage. So choose a quality smaller pad with stitched edges over a cheap large mat.