Okie-dokie, I've tested this now in 1.15 and 1.16rc5. In both revisions it is the same.
If you capture a stack you get 1NM regardless of it's size, be it one brigade with 3 regiments or 2 18 element division.
The number of VPs you get is relative to the size of the force surrendering, so a division brings about 70 VPs.
All the generals who surrender are removed from the game without any notification of their loss to either side.
You also do not get any captured equipment from the surrendering side.
I also tested what it looks like if you wait until the defender had run out of supply and then attack. The problem in a real game is that there is no way to tell exactly when that is. It depends on how much supply they are carrying (supply trains) and the amount of supply in the location where they are (depot, city with supply).
If you catch them right at the edge (not difficult when you are playing both sides by hot-seating :w00t

you can expect to get 1NM for each actual counter being destroyed. So if a defending division is made up of 4 brigades and commanded by 2 generals, if you actually kill both generals and destroy all the brigades you get 6NM and can expect a number of your generals to get a sizable boost to their seniority which if it pushes them to more than 4 above their original seniority will allow them to be promoted.
A number of times when actually attacking I also captured a battery of artillery, decimated to about 50% their original strength though.
What I find a bit unrealistic is that you get absolutely no equipment from the surrendering side. This is just my un-expert opinion. But thinking about Donelson and Vicksburg where 48 and 172 artillery pieces were surrendered respectively, it seems an oversight that in-game nothing is to be had from the surrendering side.