Mainly it would increase the current capacity. (Losses aren't appreciably affected because the voltage drop versus current curve is very steep, so the voltage drop isn't appreciably different for one diode or two in parallel.)
Also because of that steep current curve it's very important to balance the current between paralleled diodes. Otherwise most of it will flow through one of 'em and you will only get a fraction of the improvement you paid for.
With the "three bridges" hack you do this by:
- Using the two halves of one bridge for each phase (rather than one AC terminal on each of two bridges). This means your paralleled diodes are from the same manufacturing lot, tending to match the manufacturing variations, and are mounted closely together on a common heatsink, tending to match the operating temperature and its effect on voltage drop.
- Balancing the wiring resistance to the two halves, either by running a bare wire between the AC terminals and soldering the feed wire to its midpoint or by running a wire between the two AC terminals and fastening or soldering its midpoint to a terminal block where the phase line is attached (thus elimating any difference in connection resistance at the common point). This is done because a small fraction of an ohm of difference in the wiring resistance can shift a large fraction of the current to the diode on the low-resistance side, while two EQUAL small fractions of an ohm resistances feeding the two diodes can have a strong current-balancing effect even if the diodes are a tad out of match.
