Stock Pot vs. Dutch Oven / Sauce Pot

The answer is that both can be used just fine for the same purposes, however stock pots tend to have much thinner walls than the bottom and thinner than those found on Dutch ovens. The thinner walls mean that they retain less heat and so are less efficient at cooking on the stove top (e.g. soups), and more likely to burn or stick around the walls if placed in the oven - because of the faster heat transfer on these thin surfaces.

Stainless steel is more prone to sticking for some items too (e.g. eggs, meats), and is relatively difficult to season (it's generally not done to stainless), whereas cast-iron can be seasoned very easily, it's more or less mandatory for this material and essentially makes it more or less non-stick.

Enameled/ceramic-coated cast-iron pots such as the Le-Creuset ones are generally non-stick from the shop and have the same benefits as cast-iron.

Having said that I use an oven-safe stock pot for making things like pasta-bake, where it is in the oven for relatively short periods of time (~40 min - 1h), and don't generally have any problems.

If you want to do stocks I would get the stainless steel one, biggest that'll work on your stove/have room for? If you want to do soups/stews roasting frying bread casseroles ...get the dutch oven ... you can do "stocks, broths, and boiling grains/vegetables" in either.

This article by J. Kenji Lopez-Alt (from Serious Eats and author of The Food Lab) may be helpful:

I am fortunate to have a Le Creuset Dutch oven that I received as a gift from my wife. In my opinion, it beats anything else out there. I seem to recall reading (America's Test Kitchen?) that the Tramontina brand ranked second to Le Creuset and is considerably less expensive, but have not personally compared them.

Though costly, I use it for a lot of different things (i.e., pot roast; chili; braised short-ribs; etc.) and have no complaints.