From a quick survey of available on-line material - the short answer is NO, or at least there appears to be no significant difference. When you clarify butter you are just removing the milk solids and water - what remains is 100% butterfat, which contains the same fat content, calories, and at least 95+% of the cholesterol. And, surprisingly, removing the solids does not have a measurable affect on the production of LDL and HDL.
Now, if you take that process one step further and make ghee ... the cholesterol breaks down and forms cholesterol oxides (which are not found in fresh butter) that research is starting to show increases atherosclerosis.
Removing the water and milk solids helps to prolong the "room temperature" storage life of butter - there is no indication that it is any healthier.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain