I listened to the BN's Fermenters episode on the way home, its 5 year old info but I looked at the yeast book when I got home and they still agree. They say that conicals will give you reduced ferment times, lower diacetyl, increased attenuation, 'different' ester profile, and will require an adjustment to the ideal temp your used to in your carboy. They started talking about the affect of head pressure and headspace but then kind of got off track. The idea of increased beer and yeast mixing is explained that CO2 percolates from the bottom of the cone up through the center of the fermenter making kind of a fountain effect, the taller the better, which produces the results above. Its pretty tempting but at ten gallons I'll never heave it into a fridge, I'd have to build a ferment chamber or buy a heated/cooled version. Fairly pricey proposition either way.
Like you say all the above supposed improvements you should be able to overcome by other methods if they are a problem at all but if a conical does it better without having to monitor things so closely? I don't know if its worth the expense.