Plate elements are almost always easier to use. Hence, you really only want to use solids when you have to.
The big limitation with plate elements relates to the fact that you are assuming plate behavior. You can get very thick slabs of concrete that are not really appropriate to model with plates.
Example: I've got a column force applied at the top of a 10 ft thick mat and 5 feet away from that (at the bottom of the mat) I've got a pile that needs to resist that force. Is the mat going to resist the applied force through combined bending and shearing of a plate. Or, is it going to resist it through some sort of compression strut behavior between the applied load and the pile. Probably the 2nd. Therefore, even if I can get a plate mesh to work (which is doubtful with this really thick mat) then plate elements will not be capturing the true behavior of the system.
