Over pronation is a problem that plagues many runners. Before we get into discussing shoes and which options are best for helping control your foot's tendency to over pronate, you should also keep in mind other things you can do to help control it. The problem essentially comes down to problems in the biomechanical elements of the foot and ankle function during your run - meaning that the feet and ankles are not working together properly to move the body's mass forward like they would for someone who does not over pronate. The first thing I would advise would be to hit the gym - specifically, start lifting weights or focusing on strength training moves that develop and strengthen the shins, calves, and ankles. Weighted (or body weight) calf raises are an excellent option. The stronger your lower legs and ankles become, the more they will be able to support the weight of your body, especially upon high impact landing. The easiest fix would be to take some rest time away from running! Over pronation and weak arches often happen simply because of running or exercising too much, with repeated pounding. Your feet, ankles, and even your hips all get weakened and fatigued from running and play a role in over pronation. And avoid walking barefoot or wearing flip flops or other shoes with minimal support.

Now onto the shoes! Of the two you have mentioned, the Brooks Addiction are definitely the better option for both helping correct and prevent injuries from over pronation, as well as helping improve your running and running efficiency. The Brooks Addictions are extremely supportive, as they offer maximum support through a thick layer of gel cushioning and thick in-shoe 'walls' surrounding the foot (which provide much needed stability and help to keep the foot in line during runs). However, these shoes are quite expensive. But they will absolutely provide your tired arches and weak ankles with the support they need, and you can pretty much be guaranteed that they will help stop your feet from over pronating. Preventing this issue and the pain that comes along with it is priceless!

But if you want more options to choose from, continue your search with the Brooks brand. Brooks offers an entire line of different "Support Running Shoes," offering different models, styles, and varieties depending on what you need. The Addictions, Ariels, Beasts, and Adrenaline GTS models will give you the most support and cushioning. But if you want the cushioning with not such a high price tag, the Transcends and Vapors are excellent options.

Sources:
https://www.brooksrunning.com.au/support-running-shoes
https://www.orthofeet.com/blogs/news/how-to-treat-flat-feet-and-over-pronation