The double die option will add about 10 percent to the power rating as the on resistance of the mos-fet output section will be cut in half. However the main advantage of the double die option is the improvement in thermal and current capability, making the option useful driving low impedance and very difficult loads.
Bridge mode operation will essentially double the rated output power but only within the limits of the maximum recommended speaker fuses, which would be 5 amp quick blow for the Synergy 240. If these fuses are too large, then your speakers will blow first, saving you the cost of replacing fuses.

A much more economical way of obtaining higher power operation would be to acquire a Synergy 450 rather than two Synergy 240 amps and the AVA bridge.
Regards,
Frank Van Alstine