Some patients do report a decrease in libido (sex drive) when they go from not using any birth control to using a traditional birth control pill. This decreased interest in sex could be caused by the sudden shift in hormones and typically subsides once your body adjusts to your new method.
If you are switching from a birth control pill to an IUD (which delivers a lower dose of hormone locally to your uterus compared to a traditional pill), it is possible that you could notice an increase in your sex drive compared to when you were using the pill - although every woman is different. No one knows your body better than you do!
On the other side, the piece of mind you get from having an IUD could definitely affect a patient’s desire to have sex more often - now that she can do so without the fear of getting pregnant!