360 was better at running 3rd party games, making it arguably the more powerful console.

It was technically weaker from my memory, but the architecture of PS3 was tricky to work with. That being said the same thing happened the generation before. I own dozens of games on both the xbox and PS2 or the gamecube and PS2 (because of my friends preference and the most spoiled part of my childhood) and in 95% or more of the cases the PS2 version was better in terms of graphics and performance. The PS2 was considered weaker than the original Xbox and Gamecube yet was better for 3rd party games. So that being said if PS5 sells a lot better than the Xbox Series X, I could see 3rd titles eventually performing better or the same despite the hardware disadvantage if devs prioritize it. That being said, the consoles are a lot closer this generation in architecture than they were back in the PS2 or PS3 eras so it's not as much work to port things meaning XSX has a greater chance of keeping that advantage over PS5. I'm sure there are still differences, but I'm not a developer so I don't know if they are meaningful. I expect the PS5 to win the next generation and a good chance to win in the USA if they can put out good exclusives in a timely manner.