They're inherently similar. Both highly verbose and quite object oriented. Dart is less flexible and arguably less advanced, but unlike Typescript, it's sound (as in type soundness). For a very specific target (mobile) being a bit less advanced is completely fine, it has all the abstractions needed for mobile development.

Immutability is leveraged extensively in Flutter. That said, functional programming is a struggle with Dart. Although it's not particularly well suited to Typescript either. Some specific things like async stuff are better in Dart/Flutter. As Dart adheres more strongly to classes/inheritance its facilities for that are more extensive.

Dart is perhaps more Java-ish while Typescript is more C#-ish, if that makes sense.

Flutter's strength is certainly not the language, it's the SDK/platform. It's miles ahead React Native in my experience.

Take a look at some samples to get a grasp on how it looks like: https://dart.dev/guides/language/language-tour