[morzh]

Rich


Any real reason you want to do this, or it is one of those itches "I can make it better"?
BTW, looking inside, I do not see (well, of course it is not like looking at a sch) what would regulate to 25A.
I mean, I see something bolted down to the bottom on some sort of heatsink, which does not impress me as a real oomphy one.
Of course it could be that the input voltage before the LDO (which might be driving an output transistor; I do not know of LDO that is a 25A one, usually it is a transistor with LDO or a zener, or an OpAmp circuit that drives it), and the dropout is small, but even a half-volt one at 25A will dissipate 13W.
Relying on the case as a heatsink is not a good thing.
And, judging by the transformer, it is a linear supply, not a switcher.
Do you have a sch of it?

These (I've seen a few on Amazon), especially considering 13.8V output, are usually made to float Lead-acid batteries.
Also, keep in mind that 28,000uF is a lot, and I mean A LOT of capacitance. Sometimes it is really more of a number in our head, but I once made a small demo to a seasoned contractor EE who designed our power supply for a multy-dwelling modem, run from a 12V 200Ah lead-acid battery as a backup.
His board would reset the unit, and he did not understand why a measly 200uF would do that to a battery. And he did not believe me when I said that that was what did it.
To demonstrate I took a 10uF small 3mm diameter 10mm long aluminum cap, put the scope at the end of 9AWG wires that connected the unit to the battery, set the trigger at 3V (the battery was 12V) and put the 10uF cap across the scope probe. The scope triggered down to 2V.
The guy was picking his jaw off the floor and then stayed with his mouthh agape for about 15 seconds or so.

In your case, the ripple will obviously depend on the load. Do you really intend to exercise that thing to the fullest? If not, also keep in mind that the regulated supply brings the ripple down by the very act of regulation, even with a smaller capacitance. The voltage ripple transfers to the input of that regulator.
That ripple will be given the frequency of the rectifier is 120Hz, the current of 25A and the capacitance , about 7.5V. But that is at 25A. At 2.5A it will be 0.75V. No biggie for the regulated voltage input.

Doubling the capacitance will half the ripple.
And, all large caps (yours are 4700 uF) have their ripple I of a few amps, which in parallel makes it huge.

I would stick with the original, save for a situation where you clearly know you need more.