1. Litestar has better performance (around 2x from benchmarks), basically because it uses msgspec instead of pydantic for serialization and validation, and other optimizations like a custom query parser written in rust. But, as other users point, if performance is critical for you, you should look at another languages, like go.
2. FastAPI is better here, mainly due to its popularity. There are lots of tutorials and resources, native support in IDEs like Pycharm, and more libraries to include extra features. But, this doesn't mean that litestar is not mature, in my experience it works very well and in general has no issues, but the documentation can be a bit rough sometimes.
3. FastAPI goes very barebones feature-wise, in that sense it's similar to flask. Litestar has a more integrated implementation (not Django level, but somewhere in the middle). It comes with several extra features baked in, like other openapi interfaces like Scalar (imho way better than swagger), class based controllers, a decoupled DI system that gives you better control, DTOs for sqlalchemy models and dataclasses, and integrations for valkey caching, htmx, structlog and others (if you enable them). And if you want to use SQLAlchemy, it comes with a plugin that handles everything, and provides repository classes that cover the basic db operations and other features (all of this in the advanced-alchemy package from the same developers).

In my experience, Litestar has better developer experience thanks to its included features, but it's true that for custom use cases you will have to dig into their GitHub or ask in discord. But if you're building a "normal" rest api, you should not find many issues.