I've got agm batteries in my workshop and the charger I use is the same as the one I used for lead acid, but then it is an off-grid smart charger so I guess it can tell the difference (the manual does say to change settings for gel, but to leave as is for the other two types).
With lead acids that I've had, my Ctek charger has a 'reconditioning mode' which does seem to revitalise a battery that doesn't charge properly. I think it's because the high current spikes are meant to break off the sulphides that form on the lead sheets, thus allowing the battery to charge again. AGM batteries work the same, but the amperages and voltages used to spike and trickle are slightly different to lead acid (I've got the figures in a book in the workshop if you are really interested, but it is seriously dull!).
Generally though, I've found that a work out battery is just not worth the hassle or worry, just get a new one.
Also, a starting battery is not the same as a deep cycle battery. If you are starting an engine then get a battery designed for it (high cold start rating). It will work better and for longer

And get a better charger, my little 20amp (ish) Ctek wasn't a lot of money and has done sterling work for over a decade now on AGM and lead acids for tractors, caras, LED lightings and off grid battery banks