There are two completely opposing camps: one in favor of system-provided packages, and one in favor of separate installation. I'm personally in the "system packages" camp. I'll provide arguments from each side below.
Pro system packages: system packager already cares about dependency, and compliance with overall system policies (such as file layout). System packages provide security updates while still caring about not breaking compatibility - so they sometimes backport security fixes that the upstream authors did not backport. System packages are "safe" wrt. system upgrades: after a system upgrade, you probably also have a new Python version, but all your Python modules are still there if they come from a system packager. That's all personal experience with Debian.
Con system packages: not all software may be provided as a system package, or not in the latest version; installing stuff yourself into the system may break system packages. Upgrades may break your application.
Pro separate installation: Some people (in particular web application developers) argue that you absolutely need a repeatable setup, with just the packages you want, and completely decoupled from system Python. This goes beyond self-installed vs. system packages, since even for self-installed, you might still modify the system python; with the separate installation, you won't. As Lennart discusses, there are now dedicated tool chains to support this setup. People argue that only this approach can guarantee repeatable results.
Con separate installation: you need to deal with bug fixes yourself, and you need to make sure all your users use the separate installation. In the case of web applications, the latter is typically easy to achieve.