I’d say this depends in part on the soup being made.
I make soups both ways.
I’d say it is also a lot about what kind of cookware you have. If you are using cheap, lightweight cookware your results will be poorer in either method. If you have good quality, heavy, dense cookware, you will always have better results.
Using a pot you have bottom heat only and can easily see into the pot. Because you are using bottom heat you’ll probably be stirring the soup more than something in a Dutch oven. You also will have more moisture loss, especially if you have the lid off the entire time.
Using a Dutch oven you have heat all around the the contents and are losing a lower temp, so the contents cook more slowly and don’t need to be stirred or at least not often. This is a great way to cook tougher cuts of meat, say for stew, that require a long cooking time to be tender. That being said, I have done amazing soups in a dutch oven on top of the stove at very low heat with the lid on with pretty much the same results as I have in the oven, but you have to have burners you can turn down low enough and you want to be sure you don’t burn the bottom.
So...to answer your question, all else being equal, with a competent cook at the helm, assuming quality cookware in my opinion for SOME soups there would be little difference in taste or quality, possibly some difference in texture due to moisture issues, using one over the other.
Some soups would be started on the stovetop, like stew, browning the meat, then moved inside the oven for a long braise. This is what I love best about high quality cookware like enameled cast iron and heavy duty stainless, they can go from stovetop to inside the oven with no problem.
Lighter vegetable soups I am likely to do entirely on the stovetop.
One thing I have started doing in the last few years is making stock in the oven rather than on the stovetop. I’ll roast a chicken or two, strip the meat from the bones and skin leaving the bones fairly meaty (or roast chicken or turkey backs specifically to make stock with) then add all my other ingredients to the roasting pan, put the lid on, put it in a 225 oven and go to bed. In the morning I have a lovely, rich stock and it keeps the house warm all night.
I’d say the real differences are bottom vs. surround heat, temperature as I’ll likely be using a lower temp inside the oven and moisture issues as using a lid inside the oven seals in the moisture.
As for HOW I would make each version...that’s way too long of an answer if I want to get to work on time. Happy soupmaking!!!