Assuming that the Orbtronic Protected battery uses the same LG cell under the wrapper, then the Unprotected battery will have a lower resistance (because there is no protection circuit).
Therefore the Unprotected battery will enable a higher current (depending on the flashlight's driver).
That 10A is just the max continuous current that cell can "safely" handle without damage according to the supplier (or maybe the cell manufacturer).
BUT it does Not really tell you anything about it's resistance, which will limit the current an appropriate driver can draw (the higher the resistance => the lower the current)
.
So if you want maximum current/Amps get the Unprotected ones.
If you want a Protected battery then obviously get the other one.