this feature is not overly popular on 2 channel amps.
a dual power supply is normally promoted for additional crosstalk rejection. basically to help prevent one channel's transient current use from causing an audible transient in the other channels.
dual power supplies on a two channel amplifier also can also be set up to perform intelligent features, such as per-channel current limits, and possibly intelligent modulation of the power supply for some purpose (improved efficiency, equal power independent of load, per-channel protection/limiting). this doesn't mean the amp designer has actually done these things, just that it would be an option.
as for power output or efficiency, thats a mixed bag best answered by comparing the possible alternatives. By using two supplies, the power draw of each should be cut in half, allowing lower current and lower I^2 R losses. at the same time, there are potentially more switching devices and more losses due to this. alternatively, the supplies can operate in an interleaving fashion, which would allow smaller input filtering. in short, there are a handful of advantages and disadvantages that can apply.