Tire compound and tread can help reduce the risk of common road hazards -- thin layers of sand and pebbles on turns, etc.
For awhile last year I switched my hybrid from my favorite 700x42 Continental Speed Rides to 700x32 Conti Sport Contact II. While I didn't care for the ride quality of the Sport Contact II, I was surprised how well the shallow pebbly diamond/file pattern tread gripped on tricky terrain. It felt remarkably surefooted on dry sandy patches, and on wet slick roads.
On my road bikes I usually ride slicks, and there are minor differences in perceived grip between one brand or model of slicks and another. But I'm very cautious on fast curves and slower turns... at least until I know the terrain. I'm not racing and if the group gets gapped because I take curves a little slower, I'll probably catch 'em on the next climb anyway. My 61 year old bones don't bounce anymore, so I'm more cautious now.
For awhile this spring I tried an older set of Specialized Armadillo 700x23 road tires with very shallow hatched pattern tread. I was surprised how much better those gripped on wet or dry slippery stuff. And those tires were age hardened, not as grippy as they would have been new. So I just ordered a set of Continental Grand Prix Classics. I could take or leave the faux-gumwall cosmetics, but I'm curious to see how the modest tread pattern feels. I'll probably put the GP Classics on my steel bike for wet road rides.
Tire pressure matters too. Whenever a road bike ride turns onto gravel I'll stop and bleed out some tire pressure. I weigh 150 lbs so I can ride pretty low pressure without pinch flatting. Reducing 700x23 or 700x25 tires from 100-120 psi to 80-90 (lower on the front tire) helps on gravel and slick roads.