One huge difference in these two watches is the software. One runs Android Wear made by Google, and of course the Apple Watch runs its own custom software suite. The thing users need to be aware of is the Moto 360 can only be controlled via the touchscreen, or the power button on the side.
We won't get into tons of details about each operating system, as they're continuosly being improved and evolved thanks to updates.
What we will say though, is Apple nailed it with the digital crown button. Being able to control the entire interface with it, vs touching the tiny screen, is something all Android Wear devices could learn from. This keeps the small screen free of fingers, letting you view as much as possible.
With the Apple Watch you can open apps, play games, look through iPhotos and more. With Android Wear, it's not about apps, but more about information. Incoming calls, texts, doing Google searches, and getting information with a glance. The Apple Watch can do more, in a sense, with all the apps, but there are plenty of apps for Android Wear as well.
Another key difference is Apple Pay. The Apple Watch supports wireless mobile payments, while the Moto 360 does not. This isn't too big of a deal, as not too many people pay with their wrist, but it's worth mentioning.
Last but not least, is how easy things are to control. The Apple Watch will take some getting used to. Learning what does what, how to control everything, and more. With Android Wear you get a nice little tutorial, and everything is a tap or swipe away. It's very simple. Again, we'd recommend trying both before making a decision. Android Wear is also somewhat limited on iOS, and may not have all the same features users enjoy on Android.