Eye drop question please?

Hello. I have chronic dry eye and my left eye is always blood shot. I have started buying eye drops for the first time ever. The eye drops I decided to buy were generic and roughly half the price of the Visene eye drops. When I apply the generic eye drop to my eyes they clear up fast and the red goes away but a couple hours later the dry red eye is back. Do generic eye drops and brand name eye drops have a longevity difference?