Oh, how I love my EMU Stinger Lo boots.  The shearling wool is so soft that I wear these boots with no socks as indoor slippers.  I've never owned UGGs so I can't do an UGG vs. EMU comparison.  I do, however, own the EMU Stinger Lo as well as the EMU Bronte Lo, so I can provide a comparison between the two EMU styles.

The EMU Stingers are made with sheepskin and are lined with shearling wool.  In my experience, the boot runs fairly true to size (I wear a full 9) but if you wear a half-size you should round down.  With wear the shearling flattens a bit, but it also molds nicely to your foot.  The boot runs a bit wide (but not excessively so) and provides moderate arch support.

The EMU Bronte has a suede outer with a merino wool lining.  The construction of the Bronte differs from the Stinger in that it runs longer, wider and has almost no arch support.  The merino wool starts out more compact than the shearling, but it also doesn't flatten as much with wear.  Since the Bronte runs big, I originally bought a full size down (EMU only comes in full sizes, so finding the right fit can be a bit tricky).  With the smaller size my toes were crammed to the front of the boot and the suede was tight at the ankle, so I exchanged back to my regular size 9.  The fit is quite loose, but since I wear the Bronte with thick socks as an outdoor boot, the roomy fit works for me.

Overall the Stinger is the better boot.  The materials and construction are of a higher quality and the way the boot molds to your foot makes it easier to find a size that works.  I've personally been happy with my Brontes as well, but if you have narrow feet or need arch support I don't think the Brontes would work at all.  So I wear my Stingers as comfy slippers and my cheaper Brontes as outdoor snow boots, and I've been very happy with the EMU brand.