The red AW are the IMR, or Li-Mn chemistry. These are the "safer" chemistry
batteries, that don't vent with fire. In fact, very difficult to cause these to fail catastrophically.
Protected batteries are not, thus the protection circuit.
Don't be fooled too much by the mah difference between the two. The Li-Mn (IMR) batteries are capable of higher current output, which is necessary for the Provari. Even though the mah may seem smaller, it can deliver this necessary current for longer than the other protected battery.
One of the best batteries for mech mods happens to be the MNKE; its mah rating is only 1100 for the 18650, but it will crank out raw power for longer than anything else without dropping voltage near as much as its competitors. Unfortunately, they don't make it in any smaller sizes.
For your Provari, stick with the red label AWs, or other IMR battery of choice. The IMR battery is safer and will deliver the current your Provari will certainly ask for.