1. Complete the following sentences which compares yourwelf with your partner.

2. Complete the following sentences which compares you with your partner.

(Which one is correct? Do we have to use 'yourself' or'you'?)

#1 will be correct when you use 'compare' (no -s). Yes, you need to use 'yourself' (note spelling) because the word refers to the subject of the sentence. It's a reflexive pronoun.