Use either one. `pyenv install 3.x` is slower than `uv python install 3x`, but that's not the most common operation I use either of those tools for. Uv is also comparatively brand new, and while I like and use it, I'm sure plenty of shops aren't racing to switch to it.

If you already have pyenv, use it. If you don't have pyenv or uv, install uv and use that. Either one is a huge upgrade over using the default Python from your OS.

This makes sense for a desktop environment, but for a disposable testing container there is no way that building and compiling each version of Python like that is a sensible use of time/resources.

For that kind of thing I'd always either used the tagged Python images in Docker Hub or put the build step in an early layer that didn't have to re-run each time.

One other advantage is that you know the provenance of the python executable when you build it yourself. Uv downloads a prebuilt exe from https://gregoryszorc.com/docs/python-build-standalone/main/ who is a very reputable, trusted source, but it's not the official version from python.org. If you have very strict security requirements, that may be something to consider. If you use an OS other than Linux/Mac/Windows on x86/ARM, you'll have to build your own version. If you want to use readline instead of libedit, you'll have to build your own version.

I am personally fine with those limitations. All of the OSes I regularly use are covered. I'm satisfied with the indygreg source security. The libedit version works fine for me. I like that I can have a new Python version a couple seconds after asking for uv. There are still plenty of reasons why you might want to use pyenv to build it yourself.