Regarding PowerShell, I've found that it has become incredibly customizable these days. For example, I just enabled Emacs keybindings for it a couple days ago. So it feels almost like a bash terminal.
I think one of the main differences is that scoop will install for the local user. Which means you don't have to install stuff from an admin console (I think you can do that with choco but its not the default).
I also just checked to see what apps I've used in scoop vs choco and the only one that choco doesn't have (that scoop does) is wsl-ssh-agent.
scoop had all the apps I install through choco.
I'm sure theres more differences that go a little deeper, but as a simple end user, those are the only things I've noticed
The entire operation of it is simple but powerful: everything is based on a manifest file [1]. The official manifests are in git repos, but you can also install from a local file or a gist.
Chocolatey's usage of nuget packages while also basically just running the app's normal installer is weird and results in all kinds of situation where versions don't match, chocolately upgrades don't do the expected thing, etc. All these problems just don't happen with scoop (at least not in my years of experience with it).
Scoop apps install to ~/scoop/apps/<appname>/<version>/ and then get a symlink ~/scoop/apps/<appname>/current/, while also getting a ~/scoop/persist/<appname>/. It's just very elegant.
It adds "shims" for any executables in ~/scoop/shims/, and because that's the only directory added to your path (when scoop is first installed), newly added apps "just work" in all your open terminals/apps/etc.
It also seems faster. "scoop install <appname>" and a few seconds later you can use it. Chocolatey usually does the UAC prompt stuff and generally just feels clunky by comparison.
[1] https://scoop-docs.vercel.app/docs/concepts/App-Manifests.ht...