One reason to use the epoxy-based industrial floor coatings is because they are resistant to the heat and friction caused by the hot sticky tires that tread upon the surface. Ordinary porch paint won't do that (hence the results you see in your pic).
I don't think you need to remove the paint that's there now, but you do need to do an acid wash to give the next coat of paint the proper surface for adhesion. Try
www.griotsgarage.com for a superior garage coating product.
Actually when I plan to renovate my garage, I'm having a professional concrete company put down a layer of colored concrete to look like tile. Expensive as hell, but it will be worth the effort when it's done!