I also have both a standard 4 inch 629-4 and a mountain gun 629-4. As mentioned before, bevels on the cylinder is different. My standard 4 inch 629-4 also has a round butt grip frame since in mid production of the dash 4 series S&W started standardization to all round butt. Since the two examples I have are similar enough I’d say the biggest difference is the tapered barrel on the mountain gun. While it does shave off some weight, the most noticeable difference is it changes the balance to be more over the frame and cylinder rather than more weight further out front.

I also have a 629-4 with 6 inch barrel (square butt). The difference in balance from Mountain Gun to Standard 4 inch is much like the difference in balance from Standard 4 inch to the Standard 6 inch. I love them all, and they all have their virtues and compromises. Hope this makes sense.