"Peter sings better than them."
Translation:पीटर उनसे बेहतर गाता है।
Both tujhse and aapse mean 'than you' while this sentence has 'than them'.
But in case you are asking for the difference between them, tujhse is the most informal form to only be used with very close friends and family of around your age. Aapse is the formal form and can be used with people older than you, in positions of authority or strangers. There is also tumse which is intermediate formality and can be used with most people of your age or younger and people with whom you are close to.