What is the difference between the 3" & 3-1/4" 500 Nitro Express? Which of the 2 is more popular and why? Also, what is the length of the 470 Nitro Express (I assume it is one of these necked down)? Thanks for the help! Just curious.

The .470 NE is 3.25", equivalent to a necked down .500 NE 3-1/4".

The .500 NE 3" does so well with getting 2150 fps out of 570 grain bullets, at well under 40,000 psi with modern powders, that there is no reason to consider the 3-1/4" version nowadays. It might have made sense in the days of Cordite, but not any more. It would just add to the amount of filler needed nowadays.

Go with the 3" if you have a choice, but don't turn down a good deal on a 3.25...

Balisticly they are the same cartridge, the only difference being the 3 1/4" developes slightly less chamber pressure, at the same speed. That is not enough difference to make the 3 1/4" better than the 3". Most 500s today are chambered for the 3" version, and the long cases may be a bit harder to find. As Ray says, don't turn down a good deal on a 3 1/4" 500NE double!

Could you shoot the 3" version in the 3-1/4" version?

It's never a good idea to use a short case in a long chamber.

The .500 3-1/4" case length is more common in the black powder version than the nitro. Quite a number of these 3-1/4" guns have chamber damage due to firing the 3" case (the longer case became obsolete years ago which forced shooters to unwisely use the short version). This damage can cause the longer case to be difficult to extract. The same applies to the nitro version.