Fuses generally come in two types:
- Slow blow: These will sustain their maximum current, and possibly current not grossly over that, for some time. Generally on the order of a second or more.
- Fast blow: These simply blow faster than slow blow.
Fuses aren't exactly precision instruments. It is literally a piece of wire that needs to heat and vaporize. Because of this variation, fuses are rated somewhere that might be fairly far off their actual blow current. To make things more interesting, there is a curve that fuses have which shows that as the peak current increases, the time to blow decreases. It makes sense if you think of the fact that you are actually heating up a piece of metal beyond the red-hot point (briefly). The more current (energy) you dump into it, the faster you'll heat up the fusing wire.
Breakers on the other hand are more precise. Your standard AC house breaker operates by having the mains wire wrapped around a ferrous bar, turning it into a small electromagnet. When the resulting magnetic field increases to a certain point, it actually pulls on a spring-loaded mechanism inside the breaker which separates the contacts. The amount of current required to induce a magnetic field strong enough to release the latch on the contacts can be much more precisely controlled than the fusing current of a fuse.
In short, your breaker tripped first because the fuse hadn't yet heated up enough to blow. Breakers can respond sooner to overcurrents since they don't rely on something heating up, though if the overcurrent is grossly high enough I imagine that the fuse might actually overtake the breaker in speed (though it may physically detonate, if it isn't an HRC fuse).
