TLDR: Flutter made its debut at the Game Developers Conference (GDC) in San Francisco, showcasing the progress made in building games with Flutter. Over 15,000 new mobile games have been developed using Flutter in the last year. Flutter offers advantages for 2D casual games, such as being open-source, having a rich plugin ecosystem, and supporting cross-platform deployment. The future of Flutter game development includes expanded resources, smoother deployment on various platforms, and exploration of 3D capabilities.
I wouldn’t be able to compare them from a feature perspective, but it seems like Flutter itself is a cross platform general 2D app development toolkit, and people have used it to make games despite that not being its focus.
This Flutter Casual Games Toolkit looks to be a layer on top of Flutter to make that easier to do. Which is as reasonable a reason as any to create a toolkit like this.
But Godot as an engine predates the release of Flutter. So I would imagine starting fresh with no Flutter experience or jumping from Unity you would be probably better off with Godot.