This rifle is seen for most of DS9. It is little less powerful than Cardassian phaser rifle (which is calculated at 1.57 GW), has "16 beam settings, fully autonomous recharge, multiple target acquisition" and is gyrostabilized. It is also capable of automatical aiming. It is both survivability tool and weapon, much like standard hand phaser.
As mentioned above, it is "slightly less powerful" than Cardassian phaser rifle. How much is that, is, however, unclear. I would give it 1.4 to 1.5 GW output; that, however, is just wild guessing on my part.
It also has dual fire mode - standard beam, and auto-fire mode in which it fires pulses.
Presumably longer than that of hand phaser.
Type IIIb rifle is first time seen in "First Contact". Ergonomically superior to Type III a, it is much simpler design. We have only seen it to fire pulses, which could suggest that it is primarly designed for CQC (Close Quarters Combat) where rate of fire is often more important than range and precision, especially when we accaunt for pshychological stress that type of combat produces. It is equipped with scope and flashlight. Firepower seems to be reduced when compared to type IIIa, but given possible variety of settings, and fact that firepower might be frequently required, that is unclear.
EVA (extra-vehicular activity) version of typeIIIb. Trigger guard is removed, rifle butt is reshaped, and forward grip added in order to make it easier for use in EVA conditions, when one is using spacesuit with fat fingers.
This one seems to be further development of Type III B, possibly as more versatile and multi-role battlefield weapon - that is implied by fact that this type, while it never shown off-axis or widebeam setting like Type III A, and it can be safely assumed it does not have that ability, it was shown to fire both pulses and beams - hence my theory that Type III B was primarly for usage in close quarters combat which is standard when starship gets boarded, while this one is more multi-scenario weapon. In Insurrection, Picard, Worf and Data blasted hole throught cave wall - that might mean that this rifle lacks disintegration setting (indeed, I would not be surprised if it only has "stun" and "kill" settings, as opposed to 16 settings on Type III a). However, Data was holding standard hand phaser in that scene so better explanation would be that they just did not have time/will to change setting before firing.
Rifle seen in "Nemesis" is visually extremely similar to type C, with more powerful flashlight and new targeting sight, behind and above flashlight. It fired pulses in faster succession and pulses themselves were smaller than those in First Contact and Insurrection. For all intents and purposes, it seems to be just shipboard version of Type III C (something similar to M4 when compared to M16 - M4 is just smaller, carbine version of M16 optimized for CQC), possibly replacing Type III B.
