The EF 50mm f/1.4 is a great documentary and photojournalist lens. It works great starting at about f/2.0 and really shines at f/4-f-8, especially in black and white. It will do passable work at f/1.4-f/1.8 and is very cost effective for that work.
But for those looking for images that rely more on artistic expression, the EF 50mm f/1.2 is the far better lens. Wedding photographer? Environmental portraitist? Those photographers will find the color, contrast, bokeh, etc. all add up to a better image for their purposes much, if not most of the time.
I have owned both, and still currently have the 1.4 version. It was one of the first EF lenses I bought way back in the early 90's. I still have my original copy of that lens and it is still going strong, contrary to all the reports of how fragile it can be. Treat it nicely and it will work for a long, LONG time.
If the 50mm played more in my wedding and portrait shooting, I would have the L version for sure. As the OP asks, I can confirm there is just something "more" about the images I got out of the one I had for a while, when compared to images from my 1.4 version. In my estimation, it is the combination of all performance aspects that create that look. It's almost like that's what the Canon engineers were trying to do! ;-)