The bridged amps will have half the class A power, not double...
Class A is the ultimate though!
Sorry incorrect information the power on a SECA design (mine) will stay the same into 8 Ohms, but for 16 Ohm instead of say 10W we will get 20W, thus the same as in 8 Ohms non bridge. The output voltage goes up BUT the current max stays the same. BUT a P-P should give 4 times the power, this has to supply more current so in some designs the output stages will burn because of stress. (SOA)
That is why I use 16 large power transistors in my Push Pull A Class at 100W into 8 Ohms and 200W into 4 Ohms. And with a bigger Transformer I can push them to 800W into 1 Ohm a true dynamic PSU design.