Certainly with preparation of sashimi and the fish on sushi, it is very important. The manner in which the knife cuts through the meat and how the cut releases oils makes a noticeable difference. This is the same reason that there are specific cuts and shapes for each fish, to maximize the flavor.
For meat, I can say that there is certainly an effect between tearing meat and cutting cleanly through the meat. You can even see the oils and moisture being released differently. While I am not dead certain about taste being better, it stands to reason that it would be.
I am in the camp that a quality knife, and by quality, I mean a very good quality steel properly sharpened, polished and stropped, makes food preparation easier and makes for better tasting food.
I'm feeling bearish, and I'm packing a Wusthof Grand Brisket slicer from MABA
"I'm Armenian...perhaps...but then again...maybe not..."