Lead-Acid vs Lithium-Ion Rechargeable Batteries
The characteristic of these two technologies should be considered to make the best choice. As far as my experience goes, you can choose them by considering this:
Lead-Acid: (Specially sealed ones)
Pros:

Easy to use
Very stable
Low maintenance
Low cost
Suitable for standby charge mode (like in UPS, constantly in charge and used once over a long period)

Cons:

Low capacity to weight ratio
Low peak discharge current
Slow charge

Lithium-Ion: (Or similar technology like Lithium-pol)
Pros:

High peak discharge current
Fast charge
High capacity to weight ratio
Available in various compact packages
Suitable to be used in cycle use mode (mostly discharging to 50% and recharge again will be better to extend life-time)

Cons:

High maintenance
Very unstable and may explode on overcharge/over-discharge (Needs the smart parts to prevent this)
Low life cycles

So, if you're looking for a solution for cyclic use, Lithium-ion batteries will be a good solution as it has a lower weight. They provide more capacity and can be charged faster. However, you can expect about 500 life-cycle at the best condition from a lithium-ion battery. Also, it's very vulnerable to icing and cold will decrease the life-time.
But for standby use, the lithium-ion battery only will have a good life-time if you store them at 50% charge. So You will be losing much of the capacity if you need longer life-time. On the other hand, the lead-acid battery is very suitable for standby use as they have a charge mode for standby use. These batteries can be used fully charged and will have a longer life-time.