The first thing I noticed stacking them up side-by-side was that the Wing feels more natural in my hands. Not that the Classic Controller doesn't, but the ergonomic design of the Wing makes it easier to grip and more comfortable. Also, Nyko's controller is just a tad bigger, meaning its more suited to an adult's hands.
Another area the Wing succeeds over the Classic Controller is the analog sticks. The Wing's analog sticks have extra grip on them, more than the Classic Controller's single ring, meaning there's less slipping and sliding your thumbs around on the sticks. Not a huge problem, mind you, but it does help one notice the fault in Nintendo's controller.
And, finally, what of battery life? Well, to tell the truth, I haven't noticed a big difference. Since it uses a wireless dongle that attaches to the Wiimote, it uses the AA batteries in the Wiimote, as well as the AAA in the Wing. However, before using the Wing, I would generally get 8-10 hours of gameplay out of the Wiimote, depending on what I was playing, of course. With the Wing, it's about the same. To say I was surprised would be an understatement.
In the end, the Wing is a great solution. Sure, it's an extra $10 (MSRP lists it at $30, but you can find it for just a few bucks over $20 online), but you're going wireless and you're getting a controller that is more comfortable and will let you play for longer. If you've got the extra cash and are in need of a Classic Controller alternative, check out the Wing.