Tamagui has a really elegant combination of a Styling system (the mechanics of applying styles to the underlying systems), a Theming system (the way sizes/colors are passed down within different contexts of the UI), and a Component system (high level components that are ready to use out of the box). In my opinion, this is where Tamagui shines above the competition- each abstraction effectively builds upon the underlying ones, and it gives you a bunch of ready-to-use components so you can start building quickly and worry about the details later. Way better than the "just copy and paste" model of Tailwind which forces you to maintain components and manually create a consistent UI for your app.
We are using Tamagui for our open source electron app + web site. We hope to have a React Native app in the future, so we are strongly opposed to any solution that is overly tied to CSS. If you want to see an example (real-world, messy) codebase that uses Tamagui, please take a look here: https://github.com/MintterHypermedia/mintter/tree/main/front...
The biggest downside, in my experience, is the heavy/complicated/fragile setup process of Tamagui. Although this is typical of any TS monorepo. If you struggle to integrate Tamagui in your codebase, I encourage you to power through the setup phase- the payoff is totally worth it!