Almost an oil type topic there.
Some folks swear by lithium. Others, myself among them, don't feel they're worth the expense.
There are sites that about some of the advantages and drawbacks of the LI-Ions vs. SLC (Sealed Lead Acid), & AGM (Absorbed Glass Mat)
The LI-Ions are quite a bit lighter than either of the latter, but also a bit spendy.
They have noted issues in colder environments; although in another forum an Alaskan noted no issues with it for daily use. From what I've read they freeze kinda funny so I don't really trust 'em myself in that regard; though I was reading one item where if you let 'em sit of a couple secs with just the lights on then crank they work OK in cooler weather. Warms 'em up a bit...personally I dunno.
The SLC (Sealed Lead Acid) batteries are cheap. That's about it for them.
The AGM is usually the factory type of battery with YUASA being the primary supplier, but there being a lot of knock-offs that are cheaper.
AGMs are lighter than SLAs, & do better in pretty much every category than SLAs. They are what I use.
I buy 'em from YUASA off Amazon in the version that has you putting the acid in them and charging 'em. This results in a fresh battery if ya follow the instructions. You do need a charger for this. I use an old 2amp one for this I've had 'round forever or so. Seemed to work OK for the battery in one of my HDs, & my Burgman.
Do read the instructions first though. Handling acid is not hard but the cost of failure is high.
Charging is pretty easy, but if it overcharges a bit you could end up with acid coming out the top. (I have not, but it's possible)
Hope that's helpful.