Sometimes, but not automatically. A DX/APS-C sensor only uses the center of a full-frame lens’s image circle, so edge-related problems such as vignetting, distortion, chromatic aberration, and corner softness can be reduced.

However, that does not mean a full-frame lens will always give better results than a DX lens. A lens designed specifically for a crop sensor can be optimized just for that smaller area, while a full-frame lens has to perform acceptably over a larger image circle. So, for the same design effort and budget, a crop-format lens can actually perform better within the crop area.

In practice, many full-frame lenses are higher-end products, so they may outperform cheaper crop lenses—but that’s because of lens quality and price tier, not simply because they are full-frame.

There are also sensor trade-offs: if the APS-C sensor has lower total pixel count than full frame, you capture less total detail. If it has very high pixel density, it may demand more from the lens and can show more noise. So using a full-frame lens on DX can reduce some optical weaknesses, but overall image quality still depends on the specific lens and sensor.