It's hard to tell for sure from the photos, but it doesn't look like the rust is very extensive. If it's just rusty because the paint was chipped off (versus aggressive rust that bubbled through the paint,) a touch up will keep it in check, but it will always look touched up.

I happen to like patina, so I'd vote for that approach. The local powdercoater that I've dealt with charges $125 for a frame & fork including stripping.