A mealy machine in the 'pure' form is usually combinational logic combining the state register with the inputs to the FSM. So I guess because the inputs are combined combined the state register output it is more suceptible to glitches. I don't really consider the FSM type factors in glitch/glitch free outputs since the output of a moore machine can have glitches too due to various delays through combinational logic that might be between the state registers and the output. I would say mealy FSMs on average have more glitch time than moore FSMs but even that's a generalization that isn't always true.
When I design FSMs I don't even worry about what type it is. Typically I just care about simplicity and keeping combinational delays to a minimum. Whether it's a moore or mealy, if it gets the job done and hits the Fmax I want then I don't really care what type it is :)