Lithium Ion batteries can have one major advantage, up to twice the energy density of a LiPo.
They are always cylindrical and generally have a metal casing giving up some space and weight, but not much.
Even with those constraints Lithium Ion batteries normally have at least 70 percent more energy density by weight than LiPos.
This directly translates to 70 percent longer flight time (if you can use them).
The Achilles heel of the Lithium battery for our use is it's low discharge rate.
Current Lithium Ion batteries have a 2C Discharge rate and if you drain them above that rate it will damage the battery.
In fact many of the popular Lithium Ion batteries now include built in protection against charging or discharging too fast.
But for our use this only means that if you need more power than the battery is rated for it simply won't provide it.
If you are flying a multicopter and a motor needs to speed up for stability and the power is not available you have a problem.
Or if your airplane needs more power than is available, it can pull down the electronics and servos to where they won't function.
Nonetheless, the high energy density definitely justifies designing UAVs that can work within the Li Ion discharge envelope.
A properly designed copter could get 40 to 60 minute flight times and an airplane up to two hours with lithium ion batteries.
A secondary advantage of lithium ion batteries is that they can operate to over a thousand charge cycles if properly cared for.
The NCR-18650 Lithium Ion Battery pioneered by Panasonic is available in a variety of single cell energy capacities.
I challenge you to make a pack that's compatible with the 3DR Solo.