When making a suggestion, they can both be used. Use a noun after "what about" and a verb after "how about": "What shall we do tonight?" -----"How about studying?" -----"What about English? We could do some studying." When asking about something, both are OK: "I saw two films last night. The first one was good." -----"How about the other one?" -----"What about the other one?" When you want to add something which needs to be considered, you can use "what about": "I want to dance but what about our drinks? Are we just going to leave them here?"

Both are pretty close. This is how I would use the 2 differently- How about pizza tonight for dinner? What do you think about pizza tonight for dinner? With 'what about' I would use the verb, with the other you can leave out the verb.