Its all about the voltage regulator, then what the alternator is capable of producing when seeking what the voltage regulator demands, and then what the batteries can actually accept at that voltage.
Your shore charger seeks 14.X volts and can produce 45 amps and your batteries can accept that much. Yeehaw.
your alternator's Voltage Regulator only allows 13.8v and only 25 amps flow to depleted batteries at that voltage. Boooooooo!
if your VR was seeking 14.4 to 14.8 then it would ask the alternator to max out until voltage reached that high. Yeehaw!
I had a USbattery group31 which would accept 40 amps for 45 minutes when depleted before it hit 14.7v and amps would then start tapering. Saying 200Ah of somewhat healthy flooded depleted battery cannot accept more than 50 amps is NOT my experience.
I have a group27 northstar AGM
battery at 90AH, which can now, when depleted to 40% at ~400 deep cycles, accept 65 amps for 25 minutes before attaining 14.7v at which point amps taper. ~4.5 more hours at 14.7 volts are then required to near 100% charged.
When new this battery depleted to 50% could accept 106 amps from my 130 amp alternator before its voltage reached 14.7v. Now at 400 deep cycles that is down to the 80 amp range for attaining instant absorption voltage.
A 200 amp alternator and a 45 alternator will produce the same amount of juice when the target/maximum voltage allowed is 13.8v on 200Ah of battery. Perhaps the 200 amp alternator would attain 13.8v a few minutes faster, but from that point it would be the same. Big difference in amp flow comparing 13.8 vs 14.4+v.
A higher rated alternator can likely better handle the heat it generates, but not necessarily charge any faster if the voltage controller does not 'let it loose' or if the batteries cannot accept anything more than the lesser alternator can make.
The key is to seek 14.X volts when depleted, not just 13.8v. The alternator will only make as much juice as needed to raise voltage to the voltage regulator setpoint.
While 13 amps might be required to hold X amount of depleted battery capacity at 13.8v, 45 amps might be required to hold that same battery at same state of charge at 14.8v.
When time to charge well depleted batteries is limited, then a voltage regulator seeking only 13.8v is one's nemesis, and the alternator will yawn while the battery cries for more and sobs when the charging source is terminated.
Seek absorption voltage ASAP, get a voltage regulator which can ask the alternator to produce enough to attain and hold 14.4+ volts. The only time to drop voltage is when batteries are hot, or already fully charged, not when they are still depleted and time to recharge is limited.
My grid powered charging source, and Alternator, both have potentiometers so I can control voltage, and I have a very happy battery that is worked very hard and retaining capacity and performance to an impressive degree because of it. But it is not automatic. My solar also allows Absorption voltage adjustments and duration.
13.8v maximum on a depleted lead acid battery is going to charge slowly and more slowly as it slowly recharges.
With 13.8v maximum, 50% to 100% can take 24 or more hours to maximize specific gravity.
With 14.4 to 14.8v maximum 50% to 100% can be done in as little as 5.5 hours with healthy batteries.