If it helps:
(source: http://batterydata.com)
20 Advantages of Li-Ion Batteries over NiMH Batteries
Much lower self-discharge rate (except for newer Hybrio and eneloop NiMH cells, which trade low self-discharge for lower capacity)
More charge/discharge cycles
Usage pattern and charge regimen is better suited to digital cameras (and other devices where the usual pattern is partial discharge/full charge)
Self-Discharge rate is constant during the life of the battery (NiMH batteries steadily increase in self-discharge over the life of the battery)
Greater energy density by weight
Greater energy density by volume (AA batteries are not practical for sub-compact and ultra-compact cameras because of size, and AAA batteries are not practical because of capacity)
Greater number of shots per WH
Faster shot to shot times, especially when using flash
More convenient to swap and charge than AA cells (no fumbling with multiple cells, and keeping track of which battery is in which set)*
Far better cold weather performance
Far better performance at high temperatures
Devices using Li-Ion batteries are more reliable than devices using AA batteries (unlikely to have a battery door flip open and have the batteries scatter all over)*
Li-Ion batteries can be left in devices that are not used for long periods of time
Li-Ion batteries have protection circuitry built into the pack and do not rely on the charger for this protection
Accurate charge level gauge is included in most Li-Ion powered cameras, but is not possible in NiMH powered cameras (low-battery indicator only)
Li-Ion batteries do not suffer from polarity reversal
Li-Ion batteries do not suffer from the "dud" cell problem
No need to "Battery Match" cells of similar capacity
Rechargeable battery and charger come with the camera, versus buying a charger and batteries for an AA powered camera
Smaller and lighter chargers
* This advantage is over AA batteries in general, not specifically NiMH AA batteries. The advantage applies to AA batteries of other types as well (Alkaline, Lithium, etc.).
8 Advantages of NiMH Batteries over Li-Ion Batteries
Li-Ion packs are proprietary, you can't substitute disposable AA cells if your battery goes dead in the middle of nowhere, and you have no spare battery, and no AC or DC power for charging*
Longer shelf life*
Faster charging (though high-rate charging significantly reduces battery life)
AA cells will always be available, while less popular Li-Ion packs may be discontinued*
Multiple devices that use AA or AAA cells can share batteries and chargers (though there are Li-Ion chargers that can charge many different battery types by the use of adapter plates)*
NiMH AA cells can be charged from a 5 volt USB port, while larger Li-Ion packs (7.4V) cannot.
You can buy NiMH batteries at a good price from stores like Wal-Mart and Fry's but for Li-Ion you must order the battery packs from an on-line retailer that specializes in batteries in order to obtain good quality packs at good prices.
Hot Shoe Flash and Camera Can Use the Same Type of Battery
* This advantage is over Lithium-Ion batteries in general, and is not an advantage only of NiMH batteries.