Raised coop:
costs more to build
easier to predatorproof (i.e. is automatically fairly pred-proof)
immune from mud/flooding issues inside the coop
fairly easy to disinfect if necessary
floor does not develop holes, pits, etc
chickens can have access to some/all of underneath part as shelter
Dirt-floored coop:
cheaper and easier to build
harder to predatorproof vs digging predators
can flood
can't really be disinfected if you should ever need to
can become uneven and pitted, not always so easy to repair
Slab- or paver-floored coop:
All the dirt floor comments, except is expensive to build but
extremely (for slab) or fairly well (for pavers) predatorproof
There are also differences in the thermal behavior of raised coops vs coops on teh ground. However it is very complicated and hard to summarize or in some cases predict. In general, a large raised coop will get hotter sooner in summer, and colder faster in winter, than a large dirt- or slab-floored coop.
JME,
Pat