For the build-in winform controls, the difference won't be that much. In general, the rendering of these controls is pretty fast on any resolution.
Check if you are using custom painted controls. In many cases the performance is poor if the paint method is not implemented well. For example if you draw pixels (nested loops for width and height) the performance will slow down dramatically with increasing resolutions.
Another trick for custom controls is to enable double buffering, it can speed up things a lot for heavy paint routines:
public partial class YourControl : Control
{
public YourControl()
{
InitializeComponent();
this.SetStyle(
ControlStyles.UserPaint |
ControlStyles.AllPaintingInWmPaint |
ControlStyles.DoubleBuffer, true);
}