Motorcycle Lithium batteries are built with BMS that is specifically designed with a bike  charging system. That said, here are the pros and cons.

Pros
Very light weight, often smaller formfactor, doesnt leak, can be mounted every which way, even upsidedown.
BMS will cut off the battery if it falls below minimum voltage, protecting the cells (for L/A and AGM, once the battery discharges, sulfication occurs and damages the battery)
Low self discharge rate
Excellent amp draw

Cons
Equivalent Lithiums typically only have 1/2 the reserve capacity of same "sized" AGM. This is because lithium battery manufacturers follow the CCA of regular AGM to "size" the battery. My new lithium ytx14zt is 76whr, while the factory AGM is at 144whr. So read the specs carefully.
Not good in cold weather (does not apply to us, see below)
Can explode and catch fire spontaneously (hehehehehe.... especially charged when very cold) Lithiums need a short warm up to wake up (by turning on ACC and lights) before operating below freezing temperature.

So depending on your needs, if you got an infrequently used bike with inherent high standby draw (pretty much any new modern bike especially those with keyless, always on gps, security systems), Lithiums may not be suitable, but if you have a very old bike with no electronics, the low self discharge rate of lithium will be better. And all bikes will benefit from the much lighter weight.
If you have an infrequently used bike, in order to protect the L/A AGM battery, you have to invest in a trickle charger anyway. Any full discharge damage may be irreversible....as it may not charge up to full capacity anymore and it would only get worst over time. My cheap tokio Ytx9 has one full discharge and it turned into a paperweight, even using a pulse charger didn't bring it back alive. More expensive AGMs may be more resistant, but chemistry is chemistry.

Im still hoping Lithium battery manufacturers will put in a USB type C charging port so i can just stick a power bank and charge it. Sure they need a more complex dual input BMS...but I can dream.