I spent a bit of time and ISK experimenting with various Strategic cruisers for my mission running, looking at the Tengu (Heavy and HAM), Legion (Beam and Pulse), and Proteus (Rail, Blaster, Drone). (I never got a base Loki fit I was happy with, so that never got a look in.)
On paper the Blaster Proteus or Pulse Legion came out on top for DPS by a margin of over 30%. When used in practise however the extra travel time to get into range outweighed the quicker kills, plus it was more difficult to manage agro, forcing you to have a better tank. It was a similar story with a Drone based Proteus, which while somewhat more flexible, still took too long to bring DPS to bare.
So next I tried out the Rail Proteus and Beam Legion. The Legion was workable, but struggled against Frigate sized ships up close, and the fitting options did not really allow for tracking enhancements. The Rail Proteus however shone. Running two Tracking computers I can swap between tracking or range enhancements, can hit at an optimal of 84km with Spike (+33km fall off), or 23km with Antimatter (+33km fall off). I also have a flight of small and medium drones to add to the flexibility.
Against all these options however the Tengu really shone. While it generally had around 15% less DPS than the long range Rail and Beam fits, the tank was almost twice that of the rest, it could dictate range and pull agro better, and its missiles worked well on Frigates even in close orbit. Again I found the increased DPS with Hams was outweighed by increased travel times, so the Heavy Missiles won.
So now I use my main in a Heavy Missile Tengu, grabbing agro, and usually orbiting a wreck or other such object in the mission, with my alt in a Rail Proteus orbiting the Tengu with Afterburner on. On paper they can put out some 650dps between them against anything within the 10 to 50km range. While in practise the DPS is probably closer to half that, it is enough to work thought rats in an acceptably fast manner.