They are not equivalent. `sudo su` changes the values of USER, HOME, and SHELL to that of the root user. `sudo -s` only changes USER (it seems), but HOME is retained as the SUDO_USER's home directory.

Neither invocation changes the working directory, which is convenient.

Whether sudo sets $HOME depends on your /etc/sudoers configuration. Alternatively, sudo -Hs.

Indeed. I didn't know about `sudo -H`, though, so thank you.