Many types of Turing machines are used to define complexity classes, such as deterministic Turing machines, probabilistic Turing machines, non-deterministic Turing machines, quantum Turing machines, symmetric Turing machines and alternating Turing machines. They are all equally powerful in principle, but when resources (such as time or space) are bounded, some of these may be more powerful than others.
Turing machines are commonly employed to define what?  What are two factors that directly effect how powerful a Turing machine may or may not be? In the determination of complexity classes, what are two examples of types of Turing machines?