The Edge+ is much more 'premium' looking and feeling, which considering the cost it better be, and has much more advanced specs then the X does. The screen also looks a bit better as Samsung has the best screen tech but once you go past 1080p the human eye can't see a difference; it all comes down to brightness and color temperature and all that at that point. It has some more bells and whistles, the biggest being a fingerprint sensor and Samsung Pay. Fingerprint sensor is cool, though the one on my regular S6 only work about 75% of the time, but that is more a personal preference. Samsung Pay is really cool and very useful if you have a bank card that is supported. The downside is you have TouchWiz. It's better then before but still very heavy, and is likely the cause of the extreme memory management in the 2015 devices, and yeah you can replace it with a launcher but TouchWiz is always lurking. It is also the reason why any of the Samsung devices won't see Marshmallow until, at earliest, late December. If you have a carrier version you'll be lucky to see 6.0 by March.
The Moto X does not have the top of the line specs but it is also running plain old Android. The Snapdragon 808 is a flagship processor, the G4 uses it after all, and even with the LPDDR3 RAM in the Moto X the 808 is more then enough to keep the phone fast. It easily matches the Galaxy line in speed. For it's size it is very comfortable to hold in hand and the Moto features, like Moto Display, are flat our great. I'm not sure how I lived without Moto Display. I just reach for my phone and it lights up a very basic display to let me know if I have notifications. It does not sound like much but it's pretty darn awesome. You get almost pure 100% Android, which was the biggest point for me. Google has gotten stock Android to a point where it does not need a skin and the best thing I can say about it is it just works. You also get fast updates. Is there a bug Moto needs to fix? Ok, they can just push a patch out and be done. No waiting 5 months for a simple big fix while the carriers tinker. There is no bloatware. Android updates fully bypass the carriers and go right to you, usually about a month after Google pushes the code out, and if you don't like your carrier all you do is jump to a new one and call it a day. Software and lack of carrier interference is where Moto shines and that was what sold it for me. There are a few heating issues, if you do VR or heave GPU gaming then you'll run into them, but overall they aren't to bad for general use and Moto could likely correct it with a software update. There is no LED light, which some people like. Moto customer service is...dicey at best and if you are ordering from Moto Maker be prepared to wait a few weeks; they can't seem to keep up with demand right now. You don't get the little software flourishes that OEM's like Samsung put in, like better volume controls and some other tinkering that can be considered useful. If you are coming from a Nexus 6 then you would get very used to the Moto X very quickly and would keep getting the quick updates that the Nexus gets, though not quite as fast.
Both are very good phones with different pluses and minuses. For me price (~$400 vs. ~$800), stock Android, fast updates and zero carrier interference lead me to sell my S6 for the Moto X.