Absolutely not. You can say "I am smarter than him" or "I'd rather walk than jog". You do not have to use -ing after it. Than is used in comparing. So whenever you're in a situation of comparison, use than. For example: I'd love to eat cake rather than eat grapes", "I can swim quicker than you can", "I'd love to swim rather than sit here all day", "The grapes rather than the pears?", "I'd rather swim than do that" (note, than in "id rather swim than do that" means I'd rather swim, instead of the other thing, not after swimming you do 'that'.) I hope some of these sentences help you understand it better :D
Edit** Dislike my comment all you want, English grammar won't change :)
They are both correct -- gerund or bare infinitive.