Echoing others: axisymmetric analysis can only take axisymmetric input and only give axisymmetric output. If you have any doubt that your case is fully axisymmetric in both input and output... don't use it.
A circular flat plate is a good example - if you want stresses due to a uniform load, your properties are the same throughout, boundary condition is the same around the perimeter, etc... then you should get the result you want from an axisymmetric model. But if you want to look at buckling or vibration modes, the axisymmetric model can only show you the axisymmetric modes. For vibration modes, for example, you would see the first axisymmetric bending mode (the one that looks like a trampoline with a person jumping dead centre), but you wouldn't see modes where one half of the plate goes up and one goes down. Depending on your loads, you could miss very important effects.
If you'll forgive my bluntness, to my mind there's not really a "recommendation" per se - if it's appropriate to the problem you need to solve, use it; if it's not, don't. If you have any doubt, model the whole thing and see what you get. Better to do too complex a model and get a trivial result than too simple a model and get a useless one (disregarding issues of model size and computation time of course).