Re ZX600 ... Lithium batteries will not tolerate being discharged below a certain point. Some of them may have internal protection against discharge, others not. (Typical rule of thumb: you don't get what you don't pay for.)
If you are in the habit of switching your bike off with the kill switch rather than the key, you are running an ever-present risk of forgetting to turn the key off, and a lithium battery is not for you. Personally, I never use the kill switch, I turn the bike off with the key, so this is a non-issue for me.
.