I've had both Uggs and Emus, and found Uggs to be much better quality and softer. They also tend to last a lot longer. I've only had one pair of Emus, as to Three pairs of Uggs. The Emus I don't wear anymore, but all of the Uggs are still worn.
i got a pair of EMU this winter, and will never get them again.
there seems to be a hidden heel at the back of the shoe, the sizing is bit small, like 1/2 half smaller. i don't know about the durability but UGGs are better made. tho they are more expensive but they are so worth it.