I've noticed this for the first time today in Eastmarch - in the delve thing in Windhelm and some other interiors with (usually heavy) combat. There's a lag on skills taking effect - ie: press effect button, varying length of pause before the actually effect happens. And also, enemies running around like headless chickens for a few seconds before attacking, a delayed response to being hit etc.
It made the delve thing in Windhelm almost unplayable.
Never seen something this bad on XB1 before personally.
Sorry for the bad explanation - I don't really know how to effectively word this stuff.