the foremost difference intended by using conical burrs is to keep the coffee cooler and closer to the room temperature that it sits at in your hopper. this is achieved by the steep angle of the grinding surface and the slow rotation of the burr in motion. if the grinds get too hot the flavor gets affected...physically, i don't know why exactly, but it's noticeable. you will also see the grinds clump together much like they do if the grind is too fine or your burrs dull.
flat burrs grind much faster thus creating more friction and raising the temp of the coffee. keeping the blades fresh by changing often can reduce the raise in temp as well as speed up your dosing process.
some will say the grind from a conical is more consistent, but each method requires crushing the beans and the yield will always have a little dust and powder mixed in with the majority of uniform grinds.
different manufacturers also do better jobs in construction. compare the san marco sm90 grinder to the mazzer normale. the san marco has a locking button and specific settings that you must use, no in between settings. the mazzer has infinite adjustment. that's an easy one to figure out. more difficult is how the grinder is built. the tolerance in the grinding chamber is much tighter and precise in the mazzer than the often loose and floppy san marco. the resulting grind from the mazzer is much better and easier to use than the san marco.
conical grinders can have similar issues. the one i'm most familiar with is the mazzer robur. it's pretty big, well built and simple. using it yields varying results,though. adjusting the grind is more difficult than blade grinders due to the degree of angle the burrs relate to each other at, meaning it takes more time and adjustments to nail consistent pulls. this is something you can easily get used to, however. the biggest problem is that the unit was designed to grind a fairly large amount of coffee all at once to fill the doser rather than on and off to fill a portafilter for each shot. the result is an overheating grinder when used in a high volume bar scenario. this negates the effect of using a conical to keep the coffee cooler than blade grinders. i have not found a conical that i completely trust yet, perhaps someone can suggest one that they do so i can check it out.
wow, long winded and preachy. sweet.
someone back me up or shoot me down.
In short, I am in total agreement with Scott's comment and have never talked to a dissatisfied Mazzer owner.
I guess ultimately it depends on what kind of service you're going to put your grinder into, need it be a workhorse in a busy cafe, or do you need a great grinder for the morning shot in your "home cafe"?
For busy environments simply choose a good manufacturer (such as mazzer) and get the biggest baddest grinder you can with huge flat or conical burrs and a large motor. This way everything stays cooler as Scott mentions and preserves the coffee's more delicate flavors.
For home or low volume, grind on demand units are great (the mazzer mini electronic comes to mind), because you don't have stales hanging out in the doser/dispenser. The azkoyen capriccio is also a great grinder, and is more capable of on-demand dosing in higher volume environments.
I have also heard good things about the Anfim grinder, however I have not had a chance to use one. Purportedly this grinder has a smaller path from the burrs to the portafilter, cutting down on the stale residual coffee that can become trapped in "tunnel" from burrs to doser.
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