Whilst they are both usable, the more common response would be:
"And how about you?"
The phrase "And what about you?" would be more used in a situation where the person that asks how you went in an activity of sorts, you would answer the person, and if you wished to learn how they did in the same area, or in their acvtivity, you could then use both to equal effect.
But just on its own, if someone came up to you and asked, "How are you?" Personally I would feel awkward to reply with, "Fine thank you, and what about you?" Instead, I would respond by saying, "Fine thank you, and how about you?"
Long story short, what I meant was that to say "And how about you?" is more so used under circumstances where both the user and recipient of this question would be doing something and the recipient would have first asked for example, "How fast did you finish your run in?"
So, let me make it even more simpler:
Tom and Tina are talking about how they deal with problem customers:
TOM - Tina, I find it useful to let the customer know that I am serious about calling the police if they look like they are going to cause trouble, AND WHAT ABOUT YOU? How do you deal with this problem?
Actually, If Tom had asked "And how about you?" under these circumstances, it would be just as acceptable.
Now to use the phrase, "And what about you?" After one responds to the question "How are you?" is awkward to say the least.
You can use it, but it is not the common.
You can answer the question "What is your name?" by saying "My name is Moroccan Girl." Or you can simply reply, "Moroccan Girl."
How many times, even in Moroccan, would you answer that question with "My name is Moroccan Girl."? Or do you just say, "Moroccan Girl."?
Same thing applies here. You may be abe to use the phrase, "And what about you?" But to say "And how about you?" sounds WAY better and more natural.