For starters, the processors (controlling speed) are the same clocking in at 1.7 GHz (if that means anything to you). The two phones also have the same RAM, battery life, screen size... blah blah blah. So this comparison may have led people to believe that teh phone are the same, and to be completely honest, they're extremely similar. The main difference just from looking at it is the composition of the body. The HTC One has an aluminum body that is very durable and very lightweight while the Moto X is a soft plastic. If you were to throw both, the HTC One would hold up better, but not by much. Another difference is that the screen resolution is slightly better on the HTC One. Now its not huge at all, we're talking 1080p vs 720p, and most who have reviewed the Moto X testify that it doesn't look like a 720.
Even as I write the differences, many may be thinking that these are basically the same phone once again, and here is where I'm going to prove you wrong. See, the real difference between the two phones is the manufacturer: HTC vs Motorola. This matters because Motorla is owned by Google, aka the maker of Android. This allows the Moto X to have a different software design than any other smartphone. Its the first phone that you can experience what is called "full Android". For one, it has an enhanced lock screen for times when you shouldn't be looking at your phone continuously. It just looks black and displays what you need to know: texts, e-mails, notifications, etc. Another really cool feature is that the phone is always listening, for example if you say "Okay Google Now..." Google Now springs up ready to take input for a reminder, date, etc. Finally for majorly cool features, the phone can actually sense when you're driving to make navigation and reading texts more road-friendly. You can have text messages spoken out loud for example so you don't have to take your eyes off the road and potentially end up in an accident.
Overall I'd say just from the software alone and considering the fact that both phones have mostly the same hardware, that the Moto X is the phone to choose. I personally am switching in about a month and I may just write up a review after I get it.