Maybe just for the sake of clarity
/.bashrc would be a file in your root directory
/. This file could never be read by any user.
On the other hand
~/.bashrc means the
.bashrc file from the current user.
Another option is to edit the
.bashrc file in your
/etc/skel directory, this change is global and every user in the system would have it as default when created.
.bash_profile as the official docs say:
This is the preferred configuration file for configuring user
environments individually. In this file, users can add extra
configuration options or change default settings:
This file adds some per user extra variables.
PS. If we talk about security, it is not recommendable to have exec paths in your home directory, the most secure option would be to have your eclipse in some place like
/opt and as root create a symlink to the binary like:
ln -s /opt/path/to/eclipse
This will produce a link for all the users and you won't need to add this specific ( and probably dangerous ENV var for every user)