There is an advantage with AGM batteries ... they have lower internal impedance. Which - in accordance with electrical principals - means: They'll absorb a larger amount of current for any recharging voltage applied to their terminals.
I have had one set of AGM batteries in our motorhome for 8 years (and they were still serving us well when replaced just in case), and a replacement set of AGM batteries for over 2 years. To charge them we have used only the 13.8 volt stock fixed voltage converter (sometimes in parallel with a small fixed voltage charger) or the main engine alternator. Due to their lower internal impedance, the increased current absorption rate of these two sets of AGM batteries with these charging voltages has so far been all that's needed for our camping style.
When in storage during several months of the year, all these AGM batteries see is the the stock 13.8 volt converter, which does not harm them because their specified float voltage is 13.5-13.8 volts ... not 13.2 volts, as most liquid acid batteries require for floating.
Our AGM batteries only get voltages in excess of 14 volts when the main engine is running. A 3-stage charger is not needed in our situation, only the converter and the engine alternator.