I ran into this in a big way when I started honing. At that time, I had the use of a Spyderco UF ceramic stone which produces very impressively "sharp" edges which are pure hell to shave with. My feeling now is that perceived sharpness has a lot to do with the scratch pattern left by the abrasive particles, and how deep those scratches are.
The Spyderco has very hard particles embedded in an almost equally hard matrix, and leaves deep striations which are just great for catching hairs, hence the very gratifying HHT results I got from the start. Charnleys are also known for very sharp edges, and the cutting action and resulting finish appear similar from the pictures I've seen, but on a smaller scale because the grit is generally finer.
Conversely, a coticule is composed of garnets in a soft friable matrix: the garnets break down easily and any pressure seems to promote slurry formation on my example. The result is a marginally rounded edge with very fine scratches, less obviously sharp but very pleasantly smooth on the face. I find it far more difficult to get decent HHT passes with a coticule, but that doesn't mean that the shave is any worse, just different. I'm as happy with a thuringian as anything else for my own purposes now, it seems a good compromise.
What to do with a too aggressive razor then? I think Mikael and Neil have it right - strop it to buggery and see what happens. Anyway Max, which razor was it then?