Lithium batteries have undeniably come a long way in the last 3 or 4 years, to the point that except for one thing O now regard them as a viable alternative to traditional lead/acid batteries. Mind you, you do still need a 14.4 volt charge rate for most of them, fortunately with modern regulators this is easily achieved.
Lithiums offer more "punch" on start up, weigh far less than any lead based battery and they now seem to last at least as long as AGM batteries.
Which brings me to their one drawback - cost. But given time that will doubtless fade away as well. However until that happens, AGM batteries get my money.
One funny quick of lithium batteries is temperature. Last year I watched a man at Springsure totally fail to persuade his Ducati to turn over in slightly sub-zero temperatures. I suggested that if he parked it in the sun and then walked to breakfast that it would probably start when he returned - it did.
AGMs are temperature sensitive too,. It not to the same extent.