[Contains potential spoilers]
As leader of the Minutemen, I already had control of a dozen settlements or so before I joined the Brotherhood of Steel.
I started a radiant quest for the Proctor to requisition supplies from one of my settlements.
When I went to my [Minuteman-controlled] settlement, I spoke to the indicated settler, and passed an easy persuade check to convince him to donate food to the BoS. (I also saved beforehand, and tried other methods, such as paying for food, with same results).
As soon as I made the deal, I received a notification: The Brotherhood now controls this location.
Question: What are all the differences between Minutemen versus BoS being in control of a location?
I googled around and did not find a definitive answer – just lots of speculation and confusion on Reddit and Steam forums. Some folks complain they cannot built/modify the settlement at this point, but I had zero problems giving orders or building/moving turrets/walls/furniture/whatever; however, I did not try this after returning to the Proctor, only immediately after making the deal.
I checked map on my pip-boy, and still see the supply lines and it appears that I still "own" the settlement. Since it's just a radiant quest I reloaded my game until I understand exactly what I'm getting into.
Best Answer
Only some of the settlements (Roughly just over half) can be turned into allies of the Brotherhood of Steel. These select settlements can also be turned into safe houses for the railroad if they aren't already allied with the minutemen or BOS.
In terms of gameplay the Brotherhood had better weapons and equipment than the minutemen. If you haven't destroyed the Prydwen, you are far more likely to encounter a BOS patrol in the commonwealth than a Minutemen one, meaning that if your settlement is attacked you have a small chance to encounter a patrol to help you out.
You may wonder about artillery support. It may be a bug but I am able to build artillery in any of my settlements no matter what affiliation. So long as you've done the castle quest you can build them.
Ultimately they are similar enough that it's a role-playing choice for each location.