I hated doing it but, since the local stores I tried don't have Beatsx that you can demo, I bought them to see how I like them. This is my opinion based on the units I purchased and how I find them to be different.
The big differences that I see, so far, are the lack of the wires on the Airpods and the Beatsx blocking out the sounds around you. The Beatsx have the inline controls, where you can only do Siri or Pause/Play with the AirPods; though the AirPods connect faster, particularly since you don't have the On/Off button to worry about (the AirPods turn "on" when removed from the case). I've not yet adjusted to turning the Beatsx on. You need to hold the button for a second or two and, after a few seconds you'll get chimes letting you know they have connected. On a couple of occasions I've not been sure if they are just connecting a bit slow or if I didn't hold the On button long enough. By contrast, the AirPods seem to chime as soon as I put them in my ears, little to no delay.
The case for the AirPods is far superior; the case for the Beatsx cannot be "closed" and you have to kind of just shove the Beatsx into that little rubber pouch. Although I am likely being paranoid, it feels to me like just putting the Beatsx in and out of the case will eventually damage them; by contrast the AirPods case offers some real protection. The AirPods case is also less than half the size, so it is very easy to carry in a pocket anytime you go out -- I find I carry mine a lot of the time, since I'm not worried about the "bulk" in my pocket or that they will be damaged.
Battery life on both are solid. The Beatsx gives 8 hours, and can "quick charge" to give a couple of hours of listening time in 5 minutes of charge time. The AirPods only get 5 hours, but will recharge when they are in the case, with the case providing an additional 24 hours worth of charge. Also, you can use only one AirPod while the other charges.
As for sound, I find the sound different but both have fairly good quality -- which you prefer will likely depend on what you are looking for out of headphones. I've been listening to the same music on both, playing the music over and over to try and analyze the differences. The Airpods seem to have a warmer sound than the Beatsx; while the warmth sounds good to me, I think sometimes it is too warm. With the Beats, while sometimes I think it sounds more "true", other times (especially in the lower end of the mid-range) it starts sounding a bit tinny. OTOH, one song I tested starts with a solo sax and the Beatsx sounded very good to me, better than the AirPods. I think, when the sound gets "busy," the Beatsx do a slightly better job of keeping the sounds separate and clear, the AirPods on some occassions seemed to start to get a bit muddy (not bad, just not as clear as the Beats); but this only seemed to be on some songs, I haven't identified yet what kind of sounds seems to bother the AirPods).
Neither exaggerates the bass but both play bass well (unless you are wanting your bass line boosted). I'll have to listen more, but it seemed (at least on some songs) as if bass was louder on the AirPods than on the Beatsx. While I still want to do more comparisons; I think which sounds better will depend on the individual, and what they prefer from speakers. Neither are going to equal the best Bluetooth headsets; then again, either of these cost less and have smaller speakers.
In terms of making phone calls, the AirPods win easily. My one attempt at making a phone call outdoors with the Beatsx, though there was no real wind, just a mild breeze, the mic sounded like I was in high winds; I could not be heard on the other end over the wind. By contrast, the AirPods have worked really well for phone calls, as if you aren't using any type of earpiece/headphone.
I really don't think you can go wrong with either, it just depends on which work for your needs. First, obviously, it depends on if the AirPods fit your ears well. Next, if you will wear them while exercising and what type of exercise you do; the Beats are likely to stay in better, and are "safer" (less likely to lose) if you are outdoors, but the cord could get in your way for some activities. Next, if you want background noise blocked out or still want to be able to hear what is going on around you. You then have to consider if the lack of inline controls is a deal breaker; and I'll second the idea that the AirPods with an Apple Watch is a great combination, since the Watch can act as your inline controls. It just depends on what you want from your wireless earbuds.