I wanted a 5140 for the longest time but opted for the 3940 because of the dial which I personally find easier to read. Like Kari, I don't think the 3940 could be made any more perfect. It' has everything one would want on a watch. The 36mm slim case and the layout make it elegant and practical. I have worn in with a Dinner Jacket and casually on the weekend with jeans and shorts.
I understand chronographs and really appreciate them. But I like to look at my watches as functional tools and the 3940 is something I need and use everyday. Plus, it is beautifully proportioned and balanced. I don't need to time anything and while the 3970, 5970, 5270, 5004 and 5204 are all watches I would like as my next Patek (ok, the 5208 too), I'm in no rush. Don't watch this space, I'm unlikely to get the 5004, 5204 or 5208!
Whatever you choose, the. 3940 or 5140, you will love having it on your wrist. My only regret with owning the 3940J is that I don't own the 3940P as well. Or the 3979.