If you are refering to the HTC One X, seeing as this is where you talk about the One X, I would eliminate the HTC provided browser from any runnings for best browser on it. Barring the ability to access flash content, the HTC browser offers the same as the Chrome browser, just that the Chrome browser is far faster in terms of speed IMO.
Other browsers are starting to show shine, with their own versions of Incognito and syncing across devices, but I still feel the Google Chrome browser is the most streamlined and speediest offering out there. A close second would be Opera (both the mini and full versions).