It's very good on characters with shield stripping powers.
TSent, HE, SE, SI, GE all make very good use of it.
It's also a good primer with disruptor ammo. So, I use it with vorcha hunter, volus engineer, QFE, at times.
Destroyer is good because of 2 shots/clip with DM.
I like the gun, except for the time it shoots blanks. That annoys me, but not enough to make me dislike it.
I think the Executioner is a pretty average gun if you're not getting OSK on mooks. That means either using it on a class with a shield stripping power, or maybe using Phasic rounds. The kits you listed are the best ones for it, IMO. Otherwise, guns like the Paladin are better if you're going to have to 2SK.
This is my favorite Executioner build. You will OSK pretty much any Gold mook (including Phantoms) with Overload + a body shot with this build. For Platinum, you might need to switch to APIV ammo and take a Power Amp module in order to ensure OSK. Use alternating Overload and Incinerate as reload cancels for the Executioner to continuously chain tech explosions while you're firing away.
EDIT: I don't actually use the Adrenaline Mod now that I think of it - I use the Power Efficiency Module. I know it only saves like 0.36 seconds cooldown, but with Incinerate's short priming window, that can actually make the difference between a fire explosion and just Overloading a Brute like an idiot.