They each have their own pros and cons. I raise both so I will share their differences from my experience.
Cons:
As others have said, chickens are messier, noisier (even the females; the egg song is no joke), and require more space/resources. Quail (mine, anyway) are not tame at all (which makes handling for anything other than butchering difficult), egg color is limited (if you're into that sort of thing), and they can be pretty aggressive with each other when first coming into sexual maturity (even female-only coveys).
Pros:
On the other hand, chickens have distinct and entertaining personalities, lay a rainbow of egg colors, and many different breeds are available depending on your specific wants/needs. Quail, theoretically, require very little space (although the more you give them, the better, for their physical and behavioral well-being), and use very little resources for the amount of eggs/meat they provide (and given how quickly they reach maturity and begin laying/can be butchered). They are also much easier to butcher than chickens if one of your goals is to raise them for meat. All you need is a large sink and a sharp pair of shears.
I think, though, if I were pressed to choose just one to continue with, it would be chickens. I enjoy their friendliness, personalities, and those tasty, colorful eggs (still working on my rainbow).