Glenn - The Yeti's come with Deep Cycle Sealed Lead Acid (SLA) batteries and they are of the Absorbed Glass Mat (AGM) variety. The reason why I want Lithium, specifically, LiFePO4, is the superior discharge/charge characteristics of Lithium over SLA.
Essentially, with SLAs, discharge is less than 80%, while with Lithiums, you get closer to 100%. Additionally, Lithiums have a flatter discharge rate, i.e., lithiums maintain voltage from beginning to pretty much the end of the discharge cycle. Voltage drops only at the end. With SLAs, the voltage drops consistantly throughout the discharge cycle.
Charging is also faster with Lithiums, and you do get more cycle life than with SLAs.
Lithiums are also about 1/4 the weight of SLAs, so why doesn't Yeti use Lithium? Lithiums are much more expensive, and certain Lithium chemistries are more volatile. LiFePO4 is the most stable of the Lithium Ion chemistries, but they are still crazy expensive. A 100AH equivalent LiFePO4 is probably 4 figures, while a 100AH SLA/AGM, is only a fourth (or less).