興味 means an interest. 趣味 means a hobby.

趣味 means interest while the meaning of 興味 is hobby. 私と同じ興味があるのでしょうか？- I wonder if you have the same hobbies as me? あの人の趣味は本を読むことだと思います。- That person has an interest in reading books, I think. As simple as that, but I hope it helps you anyway :D