What tires are you running?
I ride on dirt/gravel roads with the S2R a little, and I don't seem to get pebbles stuck. As far as the dust staying on your tire... it is likely compromising your grip to the same extent that a layer of dust the same thickness on the road would do. Dust only stays on my tires for a couple of miles.
I'm not a good enough rider to notice a change in grip going from a set of ContiMotions to Scorpion Trails or back, on pavement or on dirt/gravel.
My father rides his 1st gen on dirt/gravel more than me, and he recently switched to the newly released Shinko 705 radials in 170/60R17 and 120/70R17. He feels much more confident on the dirt now.
http://www.chaparral-racing.com/product/shinko-705-series-dual-sport-radial-rear-tire/369-874536.aspx