갑니다, 가십니다 have the same meaning. But there's a difference in usage. 갑니다 is for showing a respect for an audience or listener. 가십니다 is for respecting a doer of an action. For example, 저는 공원에 갑니다.(I 'go to a park'.) is for showing a respect for a person who is listening to what I'm saying. 할아버지께서 공원에 가십니다.('Grandfather' go to a park.) is for respecting 'Grandfather'. -께서 was used for respecting the subject '할아버지'.

갑니다 is polite, but 가십니다 is even more polite, it's 가다 + 시 + ᄇ니다 and adding 시 after a verb makes it very polite ^^

ANSWER--->갑니다 (polite) 갑시다 (honorific) ** Good luck. ^__^