Let's look at it theoretically. Spessartine Garnet (the cutting medium in Coticules) has a hardness of 7.5 on the Mohs scale. Razor's steel hardness typically varies between 56 and 64 on the Rockwell-C scale (HRC), which is a very wide spread. If we convert HRC into Mohs, we get 5 Mohs for HRC 56, and 6 Mohs for HRC-64. Conversions were done here:
eFunda: Convert Hardness: Rockwell C-Scale
Both Mohs and Rockwell-C are non-linear scales. The differences in hardness between 56 and 64 are immense.
Bottom line, the answer is
yes, you can expect differences in performance between various steels on a Coticule. The diamonds of a DMT-plate are 10 on the Mohs scale, but those slowly become rounder over time, which affects the performance, while the Coticule works with a constant flow of fresh garnets. In practice I've not found any problems doing bevel work on either a Coticule or a DMT-E. I can say that my DMT-E is tamed enough to no longer offer better speed than a typical Coticule, and it surely is surpassed by my faster ones. When I feel the need to drop down, I usually drop down to the DMT-F. It doesn't take much time to deal with the 600 grit scratches of that hone, on a Coticule with slurry.
By all means, I'm not here to talk you into using the Coticule at all times. Whatever sets the bevel is fine of course. But you could have literally been 20 laps from home, when you decided to go to the DMT, so it's impossible to draw much conclusions here. There's one important detail to mention: the complete bevel off the DMT will shave arm hair far more easily than that off the Coticule with slurry. Off the DMT, it often even passes a HHT. I have noticed that off the Coticule with slurry, some razors really can only barely manage to shave arm hair, certainly if the slurry was on the denser side in combination with the light-pressured back&forth strokes. When I feel it's time for testing, I often optimize my slurry (meaning that I add a few drops of water if it looks rather dense) and perform about 10-20 regular X-strokes. Expecially when you notice that the razor was starting to show "arm hair" responsiveness, but it didn't improve after another round of 20-30 laps, you must suspect that the edge just maxed out on slurry.
Be my guest finding it all a bit easier on the DMT-E, I'm just trying to stay close to the original premise of this thread. ;)
So far, I personally have not found much truth in that statement. I've honed from rather soft vintage Sheffield wedges to the extremely hard TI Silverwing, over stainless steel cryohardened Friodurs and Dovos to Manganese steel Bartmanns. I have DMT's at my disposal, a selection of Belgian naturals, the Choseras 5K and 10K, and a Nakayama. I never really found any steel related rules applicable to the choice of hones and honing methods. My face can discern between the hones, but my razors can't. At least not that I'm aware of.
Best regards,
Bart.