Does anyone have any experience using non-OEM tires with their hybrids?

All four tires on our hybrid will soon need replacing, and although eco-tires supposedly give better mileage, there are times when the traction does not seem up to par. We are considering replacing the OEM eco-tires with a set of conservative 3-seasons, but don't want to do it if some unknown significant problems exist. Has anyone tried replacing the eco-tires with other tires, and if so did your mileage or driveability suffer?

Your (good) advice is appreciated. Thanks for looking.