I don't know if it's a bug or intentional, but it bothered me a lot, so I wrote a little addon. This addon increases mouse sensitivity when sprinting, so it feels like normal mouse sensitivity.
Since the mouse sensitivity in the game settings (1 to 100) and the technical value (0.1 to 1.6) have a non-linear multiplier, the addon settings differ slightly from the normal values. It's best to remember your previous setting beforehand and find the right values by trying around.
Unfortunately, with version Dragonhold (5.2.5) the sprint event has been removed, so you can no longer directly determine when the character is sprinting or not. I changed the addon to an earlier implementation. Unfortunately, this only works if sprinting is bound to SHIFT. If the ESO-API supports an alternative in the upcoming versions, I'll be happy to adapt it again.