A very high gain margin or phase margin produces stable feedback systems, however they may be sluggish in operation. If the gain margin is close to unity of the phase margin is close to zero, the system will be highly oscillatory and produce overshoots with large amplitudes that take a while to settle.
Having a gain of 6 dB or phase margin of 30 - 35 degrees will give you a relatively stable system. However there exists cases where this may not be so.
:-)