4x4 pickups usually come with tires having a more aggressive, blockier tread pattern, as a matter of style and an expectation you bought 4x4 to go off road. The more off-road the tread pattern, the more squirmy on pavement. You'll notice the difference a lot more as you push the tire's handling limits, whether by towing, fighting crosswinds, or cornering at high speeds.
Higher chassis height, larger wheel-tire diameter, taller aspect ratio are all factors that play into 4x4 vs 4x2 handling differences. Inflation pressures can also be critical for handling, although seldom adjusted for this purpose in normal driving.