In addition to the aluminium vs stainless steel case, The Apple Watch has a Sapphire crystal cover as opposed to the Apple Watch Sport's "Ion-X Glass" cover.
In addition, there are more options for bands that can be used with Apple Watch. Specifically, while the Apple Watch Sport is sold just with the Sport band, the Apple Watch is available with the Sport Band, the Classic Buckle, the Milanese Loop, the Leather Loop, the Link Bracelet, and the Modern Buckle.
However, you can purchase any band to go with your watch as every band will fit every watch. In effect, you can get the Apple Watch Sport model and then purchase the Milanese Loop to wear with it. Changing bands on all models is easy.