I created an account on this site to add my somewhat anecdotal 2 cents to help anyone else weighing this kind of comparison.
I bought the Jaybird X3 earphones in July, they had been my faithful workout/run/walk companion until last week.
To reiterate what others have correctly stated: the X3 are noise-isolating earphones geared for indoor/outdoor physical activity. If you go with the X-fit style with the earphones a tight band around the back of your neck, they will be very difficult to dislodge. They are meant to be worn completely in the ear, which will be uncomfortable depending on your tastes. I found I could wear these for hours very comfortably, almost forgetting they were there. The charge lasts as advertised, about 8 hours.
Full disclosure: I am not an audiophile. However, the provided app gives even a novice the ability to create their own, or use another, sound profile. The earphones are intentionally flat out of the box, and I found the most popular sound profile sounded best all around, so simply used that. A user can switch the sound profile depending on the song for a better listening experience but I couldn't be bothered.
Perhaps it was my particular set, but the connection didn't seem particularly strong. Indoors was usually solid, in a mid-sized busy gym I had strong connection with my phone at one end of the gym while I worked out on the other side. In my 800 sq ft apartment, the earphones would only drop connection if I had two walls between the phone and the earphones. Overall, indoor performance was very good.
Outdoors was a mixed bag, and this may have been just my particular unit. While running or walking, I wear my phone in a money belt around the waist. There would be intermittent drops/pauses but good for the most part. However, in certain areas, like my main intersection (which can be very busy) the earphones would become borderline unusable. Walking out of/to the edge of this area would usually resolve any issues but overall, outdoors bluetooth performance was good, but could become unacceptable in certain cases.
The earphones charging light stopped working a week ago, and then a couple days after that, the unit stopped working altogether. I was in the middle of a workout and it seemed like bluetooth had dropped (the music cut out) but it turned out they were dead. Charging/attempted resets didn't help, they were dead.
I got the Bose Soundsport Wireless and it's been a great experience so far. They are larger, as pointed out, but you don't really notice it. The Jaybird's are still the lowest profile/most wearable earphones I have worn, but the Bose quickly grows on you (you don't really feel the extra weight from the larger earphones). Nothing beats the Jaybird X-fit in terms of secure fit, but if worn correctly, the Bose will stay in your ears even during activity.
In terms of sound, Bose's Active EQ makes it a very simple choice for a neophyte such as myself. They simply sound better in all cases for me because I don't have a do a thing. Jaybird's app is superior but a default user such as myself doesn't need it anyway.
Bluetooth performance is a night and day affair. Indoor connectivity is even stronger, with no drops so far. Outdoors is also fantastic, there has been 1 drop, and it was noticeable only because it happened. It was over in an instant.
Very glad I found the Bose, but Jaybird support has been good. I will edit the post if the replacement pair perform better/differently.