On the PC, aiming is so much more precise. On any console, you have to wait for your crosshairs to sweep to your target so you have to be spot on with timing.
If you want to be very aware of all areas around you, you can whip around faster with the mouse than you can with a thumb stick.
On the console, all the buttons are in easy, memorable areas finding merely by touch whereas you may have to look down at your keyboard on the PC hunting for the number 4 key wasting precious time...the difference of you getting a kill or getting killed.
All this can be solved for the PC with the use of one of the macro keyboards.
All your weapons...all your perks...your online in-game well being all within easy reach and memorization.
If cost (console around 300 and gaming PC around 600-800 US) was no issue...
Advantage: PC controls FTW!
I've just added to the tally of you PC fans out there