As I showed in a, the optical image stabilization (OIS) in the Nokia Lumia 920 was a major reason I purchased one of those for myself. The new has OIS, so last weekend I tested both devices recording the same basketball game that my daughter was playing in.
I'll let you judge the results yourself in the video below, but in my opinion the HTC One did a fine job, and since that device is theI think it will be bumping the Lumia 920 out of my pocket soon.
It's fun to look at the HTC Droid DNA test results, shown in my earlier video test, and compare that video to the HTC One as well since you will see how much further advanced the camera is on the HTC One.
The HTC One isn't perfect, but it seemed to do a better job at providing more realistic color and clarity than the Lumia 920. My oldest daughter and I were each holding a device, so there are some differences in the person holding it. I actually may have been more shaky than her, given my age, and I had the HTC One in hand.
On top of just recording the video, it was very easy to capture still images while recording on the HTC One, and I was able to make some coolafter the game as well.
The Nokia Lumia 920 is a fine device with a great camera, but the HTC One does a fair job as well and can compete with the Lumia 920 for video. It's the best Android device for this type of usage so if you don't want a Windows Phone then it is a solid choice.
UPDATE: Brian Klug at AnandTech posted the best HTC One review on the Internet and as you can see in this part, he included some detailed OIS video comparisons with the Nokia Lumia 920. The Lumia 920 clearly beat the HTC One in daylight, but as I said the HTC One does a decent job and is clearly the best Android device for video recording. The HTC One shows more during the night test, but does drop frame rates a bit to capture more light.