[Mk.32]

So with "Lithion-Ion" batteries the OP mentioned I thought I would try to clear some things up.
The three types of Lithion batteries that are commonish are:

Lithium-ion
Lithium-ion polymer
Lithium iron phosphate

The first two are often used mixed up, LiPo [Lithium-ion polymer] are an evolved version of Lit-ion [Lithium-ion], and LiFePO4 [Lithium iron phosphate] are an even more evolved version.

As stated above Lit-ion batteries would not be able to provide the amp draw that is required on an FRC robot, also they are pretty dangerous [remember exploding laptops anyone] and expensive. And they are out dated compared to the new LiPo/LiFePO4 in both safety, price and power capacity.

Now I run a set of LiPo packs to power my quadcopter, these are small ones at 2.2ap/hr rated for up to 40C draw current and they costed about 17$ each, and can be charged at 8C [in 7.5mins]. Personally I love them.

However for FRC usage, LiPo packs big enough [17ap/hr] would cost easily $150+ and chargers would cost like $120 each [ones that can change them fast...] as well as the PSU to power the chargers. Also most importantly LiPos are dangerous when treated incorrectly, I have heard of people burning down houses due to charging issues/mishandling. Also they are also not nearly as tough as the lead acid packs and require more thought on mounting and protection. LiPos do however have the highest power density of most commercial batteries which is why they are popular in the RC world but with the safety risks alone they are unsuitable for FRC usage [sorry but I don't trust rookies with high explosive batteries]. However a pack that big could easily provide the power to run an FRC robot while being lighter then the lead acid battery, but the life span would also be about the same [500 cycles] making them even more price ineffective.

Lithium Iron Phosphate chemistry shows potential, but is still too new and costly. LiFePO4 has lower capacities per kilogram than Li-Po, but is inherently a much safer technology. It will not explode or catch fire if mishandled or abused.

I don't necessary agree with this, LiFEPO4 cells are price effective, very solid/safe, and rated for over 1000 cycles [Apple uses them]. But they are hard to get, not common place and have a lower power density compared to LiPo but still higher then Lead Acid. The cheapest method to get a A123 [well known brand of LiPoFE4] pack is to actually to take a part certain models of the Dewalt drill battery packs and savage the LiFePO4 cells from them and solder them up to make your own pack Click. However these are still expensive compared to lead acid, about $150 for 10ah/hr click and require an more complex charger to charge them [more $$$]. Price is the the main reason I see FRC not using LiPoFE4 for awhile.

And won't it be better to run at 100% power all the time? You would always have the motors spinning at the same speed, there would be no more variables.

I am not sure what this means, however even with LiPO/LiFePO4 batteries there is voltage drop when you draw large currents, and the voltages do flux as you use them. So you would still have to use PID/etc to account for different voltages when running things like a shooter wheel. And I doubt anyone in FRC would run there motors 100% all the time.

Also not all drill batteries are the same, some are great and last forever and some are crap and work for 5 secs [HF..] and not all Lit-ion cells are the same.