I was initially excited to play around with WebVR support for Sketchfab, after all, being able to view a ton of models in VR easily certainly sounds exciting!
However, I quickly found problems. The first of which is that I was unable to get Firefox Nightly to recognize Sketchfab for WebVR. Every other WebVR application I tried on it worked fine, but Sketchfab was never recognized (for reference, when I pressed the VR button with WebVR set up properly on Firefox Nightly, it just gave me the cardboard link). That left me with Chromium, which I tried and did recognize Sketchfab for WebVR, but is decidedly less stable than the Firefox Nightly. For example, Chromium currently doesn't limit the WebGL write access to your graphics memory, so if you have too large a model or more than one tab open which can access WebVR it crashes without throwing a proper error. This meant that every minute or two I'd have to restart Chromium. This is not ideal, and if you plan to support WebVR, you should definitely get it to work for the Firefox Nightly which is far more stable.
My next problem was that not only was positioning your viewpoint in VR incredibly hard, it was inconsistent too! This is actually two separate issues. One is that there seems to be a bug where the viewpoint is completely screwed up. With no rotation or zooming of the model I often found the models to be behind me, or super far away, or way too close, and so on. The non-VR viewport's perspective to the model had no decipherable impact on this initial pose. However moving off of the initial viewpoint in the non-VR viewport caused even more issues often times, and made it so several times I just outright lost the models from the VR viewpoint. The second issue is that the controls for looking around with the non-VR viewport don't translate to giving a good VR view. As such when the view was working correctly, it was difficult to actually get the perspective I wanted. Often times I'd try to put my head height at that of a humanoid character and be right in front of them, but that was surprisingly difficult. What I'd recommend is to instead make the VR viewport position be independent of the non-VR viewport, and when the VR mode is turned on, create an icon of the VR viewport position, then allow this to be dragged around and rotated into the point the viewer wants it in the scene. This would make it much easier to orient it correctly.
While we're on the topic of the viewport, I often found myself wanting to rotate the model while in VR mode. I'm proficient at using my keyboard while in VR, and while I know a lot of people aren't I feel like it should still be an option to drag around on the viewport area to rotate the model and change the viewport while you're in VR.
My last complaint is a weird one, but it's actually a complaint about the depth. I set up the Sketchfab WebVR after looking through the Sketchfab Oculus Rift Application. In that all of the pieces had a very nice sense of depth, regardless of your position. Shifting to WebVR, I found that even looking at the same pieces as were shown in the Sketchfab rift application, they looked flat. This makes me think that for some reason your WebVR implementation flattens the depth somehow. It's worth noting that several other WebVR pages have this problem too, not all of them, but some. Alternatively, it could be because I wasn't able to get the camera close enough to get the proper perspective for depth to be apparent.
I think that Sketchfab could benefit greatly from proper implementation of WebVR (or a sketchfab browsing app for VR headsets), however, this current implementation is extremely lackluster, and needs a lot of work. Best of luck though!