I have had a 12v Li-ion battery in my 2011 Harley-Davidson V-Rod for over 8 years, and in the 2006 Harley-Davidson V-Rod my wife rides. I wouldn't have it any other way, but it hasn't been without a few problems, mostly due to me being unfamiliar with the technology and how that manifests itself in maintenance and performance expectations.
The battery is extremely lightweight, almost like it's just a shell of a battery "for display purposes only"...Since the battery is located above the horizontal top frame, by the neck of the fork assembly, at the front of the air box (where most MC have the gas tank) having way less weight there (high) really improves handling.
Having said that, I will focus on the battery tech as it would apply to a car.
The fractional weight compared to an AGM or lead/acid battery is significant. If removing weight in general is a factor, this is definitely a leap in that direction. If you trunk locate the battery, don't expect any additional traction with the L-ion.
I would be concerned about any heat restrictions, especially under the hood or in a trunk that gets hot. You MUST determine this from the manufacturer and prevent exceeding the limit.
Buying a charger that is SPECIFICALLY for this kind of battery is a MUST. Again, check with the manufacturer and get whatever they recommend, no questions, just do it. Expect the initial cost of the battery and charger to be significant, but I think it's worthwhile, certainly for the motorcycles.
The battery I have IS subject to lose cranking power when it is cold. If you have a way to keep it from getting too cold, do it. If you're in a very cold climate and if it's cold for many months, you will have to prevent it from being cold. Again, ask the manufacturer for advice on this if your car isn't in a temperature controlled environment. They can be charged regardless of the charge level without any "memory" issues, but you shouldn't let them run down all the way or it may have to be replaced.
I'm not sure that all of that is worth the trouble for a car, but where weight is a problem, this is a good solution. Also, when properly maintained, I would expect much longer service from a L-ion than AGM or lead/acid.