Unless they have made some big changes since 2015, I wouldn't recommend one of the "drop in" replacement converter type chargers. The reason is that I believe both you and the charger should be able to control what's going on. "Three stage" is an improvement over no stages, but you can do better. I could see putting in one of those if you are in the mode of buying cheap flooded cell batteries and then just replacing them annually or maybe semi-annually. But if you want to set up a robust system for boondocking and/or long battery life, then here is what I'd look for:
Note that this is for lead-acid (flooded or AGM):
BTW, this basically applies to solar chargers as well.
1) User adjustable voltage parameters for absorb and float stage (in other words, not just three stage, but you can SET the voltage value of the stages). Different batteries want different voltages.
2) Remote (on-battery) temperature compensation. Very important. If a battery wants, say, 14.4 volts at 77º F, then the "equivalent" of that in cold temperatures will be closer to 15 volts (there is a chart). Without temperature compensation, the charger will just keep putting the 14.4 volts in. Why buy a good charger and set it up precisely if it's going to be that far off? (Tenths of a volt are huge in this case.) Even if it has temperature compensation built into the unit (but not remotely on battery) it will be far off, especially in the morning which is when you charge via solar (I have my solar controller right ON the battery box and yet at, say, 10 a.m. the charger's own temp comp will say something like 70ºF and the remote lead on the batteries will still be at like 48ºF. BIG difference -- blocks of lead don't heat and cool as fast as little chargers do. (The charger uses the remote value but the display will still show me both values so I can compare. Only very seldom do they match, and at that point I'm typically not charging anymore.)
3) How does the charger decide when to end the absorb stage and go into float? There are many ways, some better than others. "End amps" is the best (because that is the battery telling the charger exactly when it is full), but some go by time. Time can be fine if it's relatively adjustable with various parameters. Not quite as nice if it's just X hours and that's it. Some go by how long you were in bulk and estimate from there. Etc. Good to know how a particular charger is going to handle this.
4) Can you manually trigger (or shut off) equalizing? (Aka conditioning.) Can you set the voltage? Is it temperature compensated?
5) Is there a remote display? How useful is it? Do you have to dig through menus to see what you want most often? Does it show history?
6) How do the charge parameters get adjusted and can you do it conveniently (eg right from the display, or you need a Windows computer, or other adapters?)
7) What size cables can you attach and how do they get attached? You can do something with power posts and separate leads if it will only take tiny wires; but it's nicer if you can bring your nice, big cable right into the charger. Extra points for studs that take ring terminals vs. "jam the wire in and tighten a screw, then drive down the road while it vibrates."
One nice feature about going to a separate, dedicated charger is that then you can run separate wires for loads and charging (the "brown box" charger uses one set for both). The sharing of wires is what engendered the "if this buzzer is one turn the store switch on" work-around. This is because the brown box only has one slot for the wires, and so then the same set of wires is used for both charging and loads. Thus if you have the loads turned off (store switch), you can't charge (wire is blocked off). WIth separate wires (that's the "proper" way to do it) you can have the loads turned off and yet still charge. Also, you can size and fuse each job's wires accordingly (typically you can have a bit more voltage drop with the loads than you want to see with charging).
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For lithium there are some differences (and I'm no lithium expert but I did help someone install a system so I got a taste of it and I'm researching for a lithium install on a non-Chinook project).
1) They do not require temperature compensation, so no need to have that.
2) They want nearly no absorb cycle (but still many shore chargers don't let you tone it down enough at least when I was researching a few months ago).
3) You also don't want much float, so float should be adjustable time/voltage.
I notice many lithium sellers are still advocating pretty high bulk ending voltages (i.e. absorb starting) and same with float. But from what I can tell the emerging understanding is that it's better not to charge or float as high for longer life. Maybe some of it is to encourage people that it can be "drop in" with their current equipment?
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For right now, I would consider going one more round of AGM, especially if you don't have the type of situation that uses the benefits of lithium. Here are the types of things I'm thinking of:
1) Lithium are great at taking the "big punches" of high Peukert loads without staggering. This would be things like microwave ovens, air conditioners (if you have a large enough bank), and big hits like that. Lead acid (AGM, flooded) will notice these loads much more (Peukert effect). But if, like me, you don't run that type of thing (or not often), then it may not matter.
2) Lithium do not have the long absorb cycle where you are pushing wee bits of power through the eye of a needle for two hours or so. This matters not on shore power as you have 24/7 power coming in through the cord. It can matter on solar, where you are spending two of your precious sun hours poking wee bits of power into the battery
(On the other hand, it may not actually matter, depending on size of battery bank, solar array, usage, location; but it's something to think about.)
3) Lithium are lighter weight. Lightness is nice, but for example in my Chinook another 100+ lbs is not a big concern. Also they can take up less space. Not because they are so small but because you can use them down to 20% (vs. 50% recommended for lead-acid) so you don't need as many.
4) Lithium don't mind partial states of charge (PSOC). You can go from 30% to 85% then back down to 40% and up to 70% etc. all the time. No big. Lead acid (especially AGM) want to be fully charged as often as possible. They don't "like" PSOC (although there are carbon-foam AGM's that do better with this, such as Dragonfly brand).
5) Lithium hate heat (even more than lead-acid). They also cannot be charged when they are below freezing (loads can be run though). This may be an issue in certain climates, especially if keeping the batteries in the outside compartment.
6) There can be some .... shall we say differing info or philosophies... on how best to treat/charge lithium batteries. With flooded or AGM, it's pretty well set by now how it's best to treat them. I have to admit, I'm one of the people who is driven a bit nuts by the idea of buying $3,000 worth of batteries and then having to figure out which of the conflicting charging theories to follow (Ahh, Lifeline and their cut-and-dried manual that explains just what to do.) I think I have mostly figured it out, but it can still be annoying/stressful if you are a certain personality type.
7) If you make a mistake it costs even more
So, as usual, there is no one best answer, IMO. It depends on your usage type, budget, and inclination. I'm not buying batteries for the Chinook right now (4.5-year-old AGM bank still happily supplying power), but if I were? For my use case, and my underweight Chinook, I'd probably stay with AGM. But for another project I'm working on now, I'm probably going to choose lithium because the considerations are different.
Also as usual, this is all just in my amateur opinion
