I think it comes down to the perceived future of the language more than anything.

Dart support is pretty poor. You can compile to JavaScript, but that adds friction. Browsers don't support it directly, and probably never will. It seems like there's a pretty decent chance that Dart will be dead within a few years, at which point any time invested into it will have been somewhat wasted.

Swift support is pretty good. It's completely integrated into Apple's toolchain, and writing an app in Swift today is just like writing an app in Objective-C. Apple's throwing their weight behind it and there's zero chance that it will go away anytime soon. Putting time into it carries zero risk as long as you think you'll want to continue to target Apple platforms.

This is the upside of Apple's dictatorial "I am the platform!" model. If they decide that the platform shall support a new language, then the platform shall support a new language. On June 1st, the main language for development on Apple platforms was Objective-C. On June 2nd, it was Objective-C and Swift, just like that.

No company can swoop in and impose something like that on the web. This is generally a good thing, as one company can't fuck it up for everybody. But there are disadvantages, like it being really really hard to push a good new language.