Grabby refers to brakes not traction.
If your tire's tread is causing traction issues,nothing you do with the brakes will fix that. You need to run different tires. I always advise the folks who come to my clinic with cross and MTB's to switch to street tires if they're not going off-road or riding in snow.
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C'dale BBU('05 and '09)/Super Six/Hooligan8and 3,Kona Dew Deluxe,Novara Buzz/Safari,Surly Big Dummy,Marin Pt Reyes,Giant Defy 1,Schwinn DBX SuperSport,Dahon Speed Pro TT,Brompton S6L/S2E-X