Peter,
I ran the Shure on my Rega P3 for two years and replaced it with the Dyna about two months ago. You can click on my system link to see what kind of gear I'm using, and it will be clear that my priorities are not neutrality or transparancy, but rather a rich, smooth, enjoyable presentation. In fact, my system isn't really resolving enough to highlight dramatic differences between cables and such. Not surprisingly then, I didn't find huge differences between the two, though I ended up staying with the Dyna. Here's my assessment, then:
The Dyna's bass seems a bit flabby in comparison to the Shure. The Dyna has a richer midrange and more "sparkely" highs. Both are very quiet, with maybe a slight edge to the Dyna. The Shure is a better tracker, though the Dyna is no slouch in this area. The stylus of the Shure seemed to attract gunk more readily than does the Dyna. The Dyna seemed more sensitive to VTA than the Shure. The Shure has a user-replacable stylus and is easier to mount to the arm. The Dyna is better looking.
In summary, I found the Shure to be more lean/transparent, while the Dyna seem more lively. I liked them both and could have easily lived with the Shure for a couple more years.
Like so many things, I suppose, the right choice depends on what you're looking for. Good luck and have fun.
P.S. the Shure's for sale--let me know if you're interested