Stallman would probably use GNU wget which is licensed under the terms of the GPL, while curl is licensed under a license derived from MIT/X consortium.
On the other hand, I think I've read a FAQ where he says he views web pages by having a script fetch the pages with wget and them emailing them to him, but I'm pretty sure that's simply because wget is free and does the job (being able to recursively download the necessary resources), not because it's GPL licensed.