In fact, if one has sufficient savings and has no worries about career, quitting the full-time job also makes a lot of time/energy for the kids. That's pretty drastic, but I'd consider it myself in the future.
A middle road is working from home on your own startup/bootstrapped company, or even just freelance work. You might forgo income and career advancement, but you may just reap the rewards of more success with your children.
I'm not suggesting you're falling for this mistake but working from home does not equal being a stay-at-home parent.
If you're concentrating on a startup or freelance work then you're not giving your kids your attention. It's not enough to be there, it's better than not being there but don't fool yourself that you're bringing them up just because you're in the same building more often.
Highly recommended, if you can swing it, at least once.
Now, how to get back in the work-force...