An auto transformer has the primary and secondary windings electrically joined and the isolation transformer has the primary and secondary windings...isolated.
The AT will transmit electrical noise while the IT will not (as much). A shielded isolation transformer offers the highest level of power line noise isolation. How "critical" depends on your application - if your wiring system is noise-free, an AT is sufficent. If you have a lot of computers, digital, motors, EMI, RF etc. in your system, then an isolation xfmr would be the way to go. Best way to do it is whole-house or whole circuit rather than at the equipment.
The AT will transmit electrical noise while the IT will not (as much). A shielded isolation transformer offers the highest level of power line noise isolation. How "critical" depends on your application - if your wiring system is noise-free, an AT is sufficent. If you have a lot of computers, digital, motors, EMI, RF etc. in your system, then an isolation xfmr would be the way to go. Best way to do it is whole-house or whole circuit rather than at the equipment.