This is one that’s down to personal choice.
Cotton drill is the original fabric for painters’ whites and it has a soft handle which feels comfortable against your skin. It’s fairly absorbent, so spots of paint won’t wipe off easily, so it gets dirtier more quickly.
Polycotton is a durable fabric that doesn’t feel as soft as cotton, but it’s less absorbent so it generally looks better for longer. Plus you can add a stain-resistant coating to it, like on ProDec Advance Trousers and Bib & Brace, which enhances this even more.