I use LF for the tonality, detail, the contemplative way of working, the control, the large groundglass "viewfinder", the versatility, the ability to make decent size grainless prints with smooth tonality and extreme detail, and the possibility of using vastly different lens types each of which have their own character. I also enjoy the equipment - the wood cameras and so on.
Edit - I like challenges. I like knowing that it's up to me to use the equipment to (or near) it's potential.
Using LF has also made me a much better photographer, regardless of the format I'm using. One of the first things I learned from LF was pre-visualisation, that is knowing what the print will look like before I expose the negative. This is a valuable skill with any size camera.