Neither is as lightweight as native, but if you've got a collection of apps running against OS webviews vs a collection of apps running against their own Chromiums, it seems like the webview ones would share at least some memory. (It could just be that all you gain is disk space and smaller downloads, which I agree isn't that much of a win)
When I was playing with Tauri I had to install libwebkitgtk etc for it, since neither firefox nor chrome brings in that dependency. Unless you're using some gtk browser that disk space was not saved by Tauri at all.
Anyways other than Tauri is a Rust-flavor, on the resource usage side, it shall not have much difference from using Electron, which uses Nodejs.