When comparing Debian Kit vs GNURoot, the Slant community recommends Debian Kit for most people. In the question“What are the best ways to run Linux applications on Android?” Debian Kit is ranked 5th while GNURoot is ranked 11th.
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Pros
Pro Does not require a rooted phone
GNURoot is a completely self-contained app that cleanly uninstalls and doesn't need root permissions.
Pro Includes a VNC client for GUI apps
Setting it up takes some effort. And 3rd-party VNC client (or X server) apps might have a better user interface than GNURoot's default. These also work, but also take some effort to set up.
Cons
Con Requires root permissions
Debian Kit is not even chrooted. It's a side-by-side install with full direct access to Android's filesystem.
Con Wakelocks on by default
It drains the battery pretty quickly when running.
Con Requires a lot of manual configuration
GNURoot doesn't hold your hand and isn't even documented very well. Getting anything graphical to run takes some doing.