The hardware in the original mini is almost three years old. The A5 SoC was introduced in 2011 with the iPad 2, and has since been surpassed by the A6 and A7, both with twice the RAM as the A5. It's unlikely that Apple will spend much effort optimizing iOS 8 for the A5, and as apps begin taking more advantage of the A6 and A7, the apps will begin to feel slower on the original mini. The retina iPad mini is essentially two generations newer, making it a much better buy if you're interested in longevity. And as others have noted, the screen is MUCH better for web browsing!
I think the iPad air would be better for web browsing with the iPad mini. You would have two zoom in a lot How ever I think the iPad mini would be better for gaming on the the iPad air would has the iPad mini would be a lot lighter