I have a D-Moll and mainly use a custom made Langraff Dynamic Overdrive. Mine is slightly different from the stock models in that the toggle affects compression instead of voicing. Landgraff pedals run probably about $100 more than typical boutique overdrives, but I own many overdrives and this is the best. My personal favorite has always been the OD-820 which would be my 2nd suggestion, but the Landgraff just has some magic you can't find in other overdrives. All I have to do is set the tone and output knobs to noon and the drive all the way down and it dynamically enhances whatever amp I play through. I don't know how he does it, but it really does seem to magically adapt to any amp. It also has a little more overdrive on tap than typical tube screamers if you use the middle toggle position (Marshall mode I think). It also has a clean boost thing in the upper toggle position.
Just for reference, I can tell you that I own the following overdrive pedals:
Landgraff DO custom, Maxon OD-820, Maxon OD808 & OD9, BBE Plus, Ibanez TS808 handwired, Klon Centaur (silver), Maxon TBO9, T-Rex Alberta, and Plush Cream. I own other pedals but they are more in the distortion category such as the Wampler Sovereign and Bogner XTC Red, so they don't necessarily make good "always on" pedals.
I'm sure there are always those who say tube screamers are all the same, etc... but I own many and disagree. Though they can be very, very similar, and may even audibly be identical, there's always a difference in feel, compression, and how they interact with amps. I'm no expert but that's what I think.