Mostel,
I would have to say no. I love Rolex also, but there is no way I would sell a 3940 for a Day Date Platinum. I love the DD and have an Uncle and several friends who own one. Beautiful watch and the weight is really what makes it special. But the Patek is truly beautiful. A masterpiece of craftsmanship, detailing and elegance.
I don't know if this is the right analogy and forgive me if it is not, but if I had a choice of a Mercedes Benz S Class or an Bentley Arnage at the same cost, no way would I pick the S Class. I should point out that I own a S Class already, so I do like the car.
I don't know if you need an everyday watch that is tougher than the Patek, but if that is what has prompted your current line of thinking, I would say keep the Patek and buy an steel Datejust. The additional cost is minimal compared to the Day Date and you have the best of both worlds.
Yash
p.s what metal is the 3940?