I really doubt that you were getting better cooling with the stock one, especially knowing how terrible the stock coolers are. Maybe there were bad readings from the sensors but for sure it wasn`t better that this one, that aside the H80i is a closed loop cooler is not really the best one on the market, it`s strongest point over the stock ones is that you can have decent temperatures while overclocking with minimal sound noises. A normal cooler will have to rev up trying to keep your CPU cool thus making lots of noise and maybe failing to cool an OC CPU anyway.
For example mine never goes above 55°C while rendering in Adobe Premiere Pro for more than 30 mins (all cores to 100%) and this with fixed 600 rpm on my fans, stock one would rev up like a jet and had temps around 65°C.
If you really want lower temps, though 45°C is quite ok for normal use, i get that while playing BF4, you`ll have to go for H100i or other more expensive cooling solutions, but it would be pointless.