I want to either paint or stain a new patio. Which process is easier?

Either one should be just as easy Cathy. They make stains and paints specifically designed for concrete and wood decking (not sure which you have). Each of these products just roll out using a roller with a long handle. They are available at Home Depot.

Yes I agree that it is the same difficulty level applying. The only thing you may want to consider is how each will look in a couple of years when it is weathered. Stained decks will fade in certain spots, while the paint will have chipping. It may be easier to re-stain rather than re-paint in the long run.

Thanks