I am very familiar with both suburbs and they both have their perks! I guess it really depends on your lifestyle?
I would say if you are a foodie and love to go for walks around stunning gardens and venture through streets crowded with large homes and trees South Yarra is a very glamorous and bustling place to feel special in.
Hampton is the ultimate beachside safe and community driven suburb. In close proximity to Brighton and the beautiful beaches and cafes you have the walks and coffee vibes as well as heaps of community based elements to a wonderful suburb. If you have a dog hampton is the place to be ;)
Hope this helps a bit, call me if you need any real estate advice!