The 'simple' answer to this is: a resonator is much less stable than a crystal. In terms, they are also less precise (look a the tolerance on the datasheets).
Long geeky answer:
The external ceramic resonator is less expensive, and less accurate than an external crystal. It is usually a 3 wire device, the third lead going to ground.
An external crystal is more accurate than a resonator. It requires two, identical, external capacitors tied to ground. They are more expensive than resonators. They come is a wide range of accuracies.
If you are more a list person:
Resonators:
- not that sensitive component
- smaller
- less accurate (say, 0.1%-1.0%)
- cheaper
- may have internal capacitors or need external ones
- good for low speed serial port comms
- better ESD tolerance
- better shock/vibration tolerance
- not very suitable for a RTC/timekeeping/wall clock
crystals:
- quite sensitive component
- bigger
- more accurate (10ppm-1000ppm)
- more expensive
- needs external capacitors, their value depend on what crystal is designed to work with
- does not like ESD
- does not like shock/vibration