The HTC One X is still sharper even after the update. I posted 2 shots below which illustrate both phones in Auto mode. The Lumia shot is post-update. It is a well lit nightstand and the difference in detail is fairly obvious. However, the One X is still noisier. The One X is always noisier/grainier and that is really the most noticeable flaw of that camera...especially when shooting people. It is also terrible in low light. The Lumia's main flaw IMO is that it has piss poor automatic white balance. You are constantly getting greenish shots like the one below. To compensate I will often select Fluorescent in the white balance menu to get a warmer shot.
The One X's forte is shooting stationary objects in good lighting. I have had major difficulty with the One X focusing on a relatively close moving object, such as a child. It is hard to get a good lock, and using the burst mode degrades the quality considerably. Taking single shots I end up with a few excellent photos mixed in with a bunch of blurry, unfocused shots. The Lumia 920 focus is excellent by comparison. Seriously, I never have a focus problem.
In low light the difference is magnified due to the lack of OIS on the One X. Minor hand motions blur the shot so you have to be absolutely still to get a good one. OIS on the Lumia eliminates this problem almost every time. If the object is moving you will still have motion blur on either phone.
Another advantage to the Lumia is just the mechanical advantage of having the shutter button. I can focus on the subject then wait for the shot I want, then fully depress the key to take the shot quickly. Or you have the option to single press to focus and take the shot. The One X you have to tap to focus, then tap another icon to take the shot. It is almost impossible to use effectively with one hand, especially without introducing hand shake blur.
Note: above I mentioned the hazy/light bleeding appearance of the HTC One X outside. Well, afterward I noticed that had been shooting with a oily lens. I have found since that the One X is EXTREMELY sensitive to any sort of smudges or oils on the lens. It must be perfectly clean. The Lumia is a bit more forgiving in this regard.