Going from knobblies to slicks is the single biggest improvement you can make for riding on the road.
Knobbles are like small bumps that suck your energy and turn it into noise.
Slicks are narrower, so can take a higher pressure which reduces rolling resistance.
The width thing is a bit more complex. At the same pressure a wider slick has a lower rolling resistance, BUT narrower tyres can generally take higher pressures.
For distance riding, a slick of 1.25 to 1.5", pumped to its max will be effective.
My touring partner had fat knobblies. When one burst, I convinced her to change to slicks and she was amazed at the difference, and was still able to use them on trails.