I've had better results with the Clorox due to the quality of the wipe themselves. They also stay wet longer and don't dry out. The smell is usually better as well, but otherwise, I feel they can be about the same!
The store brands to me don't clean all that well, but with Clorox it cleans perfect. I'm not sure if there is a difference in the cleaning chemicals that they put in there but it just cleans better for me.