Quite correct, Monty's info is out of date.
Some of the highest battery energy densities and capacities are found in certain Li formulations, and best performance is achieved at very low drain (1-5 mA). Recently the best of them can handle higher continuous current draws, enough to power LED's, but at the cost of lowered total capacity.
Unfortunately, many of these battery types are not sold retail, and are only used by the military, in remote sensing devices, or other high-tech equipment (I found one interesting battery at a great price, but minimum order was 50 batteries).
See the SAFT web site for all the information you've ever wanted about a many Li battery types.