There are quite a few Lithium battery technologies knocking around typically derived from Lithium Ion. Lithium Polymer (LiPo) and Lithium Iron Phosphate (LiFePO4) are what is allowed for use in fighting robots.

Although the modern, e.g. Optipower LiPo cells have better performance you do need to be more careful to charge them correctly and protect the cells properly. LiPo cells are less durable and puncturing them will result in fire. There are specific additional requirements when using LiPo cells and you do need to make sure they are sized correctly to prevent over-discharge.

LiFePO4 offer good performance and are safer and more tolerant to over discharge. However, when used properly, LiPo come out ahead.

Other Lithium batteries aren't really commercially available for our use and due to the safety concerns are not allowed.