I believe they can be used interchangeably, there is a lot of overlap between the two, but personally I would prefer to use; "How about" when making a suggestion that I feel is best. "What about" when I am less set on the idea and more willing to listen to other suggestions. *What about can also express an objection, whereas how about does not.* "How about going to a movie?" - "I would love to, but what about the kids?" [meaning, we would have to arrange for their care.]

Hello! In how I see it, 'how about' is more about a suggestion. For example "how about eating your vegetables?" Or "how about seeing a movie?" 'What about' is more of starting a question that is asking about something that was left out. For example "what about me" or "what about feeding the goldfish". It can be used for a question that is asking about a limitation. "What about the budget? We need to save money." Hope this is clear and is helpful!