AC advantages: easy to step voltage up and down with minimal losses in efficiency, some components work really well with it (any motor that needs to run at a constant speed, lots of avionics components).
AC cons: I'm pretty sure it's witchcraft with all that current leading or lagging voltage and parallel RLC circuit nonsense, AC motors aren't optimal for all applications, you have to have monkey motion like CSD units or solid-state VSCFs to keep a constant frequency as engine rpm changes, did I mention it's like voodoo?, you can't really store AC in a battery.
DC advantages and disadvantages are pretty much opposite of AC.
Alternator vs generator is kind of semantics, in this context I'm guessing that the desired answer is that a generator pumps out AC while an alternator has a built in rectifier so it puts out DC. However in GA land a generator is a device that puts out DC via brushes and a commutator instead of slip rings and a rectifier.