The original rectifier boards have the two bridge rectifiers soldered under the PCB where they mount to the large metal base plate that provides a massive heatsink.
http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#How_To_Properly_Mount_a_Bally_AS-2518-54_Rectifier_Board

Sounds like you have an aftermarket rectifier board with the bridge mounted above the PCB and a small heatsink on top.

Guess which solution is going to run cooler.

Are the rectifier boards identical between the two machines?

probably the feature lamp bridge. it usually gets hottest by far in normal conditions.

These transformers found in later bally games run pretty high voltage to the feature lamps. A few games like kings of steel and black pyramid i have picked up had all the lamps blackened and mostly burned out when i got it. There was over 7v going going to the feature lamps. 1volt difference between the two games would result in a lot more heat at the bridge for the higher voltage one.

Stick a big hunk of finned aluminum to it for a heat sink. You can buy one from China for like a buck. Might have to drill a hole to mount, but it will help your bridge survive.

https://www.aliexpress.com/item/Centechia-DIY-aluminum-Heatsink-radiator-heat-sink-Ddesigned-for-high-power-household-LED-light-or-fish/32828383319.html

Is the game with the hot feature lamp bridge running incandescent lamps while the other game with cooler bridge running LEDs?
Incandescent lamps draw much more current, as a result its bridge rectifier will be more hotter.

Incandescent lamps draw around 0.25 amps.
There are 90 odd feature lamps in this game.
Worst case with all feature lamps on, 90 times 0.25 is 22.5 amps being drawn from the feature lamp supply.
Presuming the diodes in the bridge rectifier have a voltage drop of 0.5 volts, with two diodes in series you lose 1 volt across the bridge.

1 volt times 22.5 amps means the bridge could potentially dissipate 22.5 watts!

Compare to running all LEDs. Standard LEDs draw 0.02 amps. SMD LEDs draw around 0.06 amps.

90 times 0.06 is 5.4 amps.
1 volt times 5.4 amps means the bridge could dissipate 5.4 watts (with all feature lamp LEDs on).

The game with incandescent lamps in the feature lamps is causing the bridge to dissipate 4 times the power compared to the game with LEDs in the feature lamps! That's why it's running much hotter. The thin aluminum heatsink is not sufficient enough to disperse the heat.

What brand of rectifier boards have you got? (you mentioned both machines had the same board fitted).
The rectifier board in your picture above has LED indicators for all the supply rails. Neither the Rottendog you mentioned, nor the board in the ebay link has LED indicators.

Decades ago I’d externally wired my EBD bridges to the big mounting plate after the feature lamp one had burned out a second time. I think what must have happened was the bridges had been replaced on top by the previous owner and I didn’t know that was wrong. Can the same bridge work whether soldered onto the top or bottom, I’m not sure. It was before you could find out everything on the internet in two seconds and so long ago my memory is foggy as to how it all transpired. But I recently put in a Rottendog board so now it’s only a memory anyway. 8D