I had thought the proper version would be something like "what do you love most/best about me?". Before translating, I just wanted to say this. If I am mistaken, just forget it.
Sorry, too late... I am not usually online in the weekend. Anyway, as far as I know both 'the most' and 'most' are possible. As is 'best'. I agree that 'the most' is less commonly used than the others, but I don't think it's wrong.