What game types would you consider Unity to have better performance and/or tooling for? Also, if you're feeling generous, why?
The main difference IMO is that Unity has become the de facto standard for anything VR related. UE is doing a good job with their VR support too, but it's really clear which engine is favored by SteamVR, the Oculus SDK, and the community at large.
Unity also has a first class asset store which can save you months of development time when it comes to things like networking or doing complex shaders.
Other than that it really comes down to personal preference. Scripting with Unity vs. Blueprints with UE, C++ vs C#, etc.
Unity started out targeting low-end PC, then got into mobile a long time ago when mobile was very weak. So, naturally it used very basic techniques that are crappy but fast. Over time, Unity has been adding more and more advanced tech.
UE is the opposite story. It started out targeting consoles and high-end PC. It started targeting mobile when mobile was already pretty capable. At first, the tech it used was not feasible on mobile. But, over time the perf improvements of UE and mobile hardware have been converging.