BEWARE of "bigger/more" is better. There are some crap batteries (Ultrafire being a poster child for the breed) that will claim, 4000, 5000 > all the way up to 9000mA!!!! for a 18650.
THERE ARE NO SUCH BATTERIES! 18560 of major brand names (Panasonic, Sony, LG, Samsung) max out at 3400mA. Even then if you check them they are generally 3200-3300mA.
A protected battery is simply one of these cells that has a protection circuit 'grafted' on to it, which makes it.....longer....and if the way this circuit is applied there may be a thin strip down the side under the shrink wrap connecting positive to negative. This makes it a tad bigger diameter. A few lights may not take well to the extra length and diameter.
If you have any slop at all in your stock battery case, this should not be a problem.
NOTE - native Panasonic batteries do not have a protection circuit. That is placed afterward by some other entity. This modification is a common practice and not necessarily indicative of any problem.