Phase difference only applies in 3 phase circuits, houses are single phase. If you are stating one outlet is on other hot side (240 volts across both hot wires) vs both on one side (120 volts across to ground), it would not make any difference as the power supply on either configuration just converts AC to DC with the power supply capacitors storing the energy long term beyond the 60Hz.
Why is it necessary to have gear on the same phase from electrical panel?
The source of power from any circuit is 120 V - therefore having some circuits on a different phase Side from the panel would seem OK.
It sounds nice to have everything on the same phase but does it really matter?
The only thing I can think of that would improve things is to keep all the noisy stuff on one side of the panel, like refrigerator, and the cleaner stuff on the other side.