I've done both the "work and start a start-up" and the "quit and start a start-up" thing, and I wouldn't ever do the double work thing again.
When you're first starting a tech start-up you need to go through an intensely creative period to help you figure out what exactly you're going to do at the beginning. After that you need to put a ton of time into making things happen.
In my experience, your day job will suck so much life out of you that your start-up will pay a huge price during this crucial early period.