When you ship a binary, it’s good to provide means for the users to accommodate the binary to the specifics of their own system, among other things, adjusting library search paths.
A user can generally tweak LD_LIBRARY_PATH and /etc/ld.so.conf, both of which are with lower precedence than DT_RPATH, i.e. you can’t override what is hardcoded in the binary, whereas if you use DT_RUNPATH instead, a user can override it with LD_LIBRARY_PATH.
(FWIW, I think ld.so.conf should also take precedence over DT_RUNPATH, but, anyway, at least we’ve got LD_LIBRARY_PATH).
Also, I strongly disagree with the suggestion above to use DT_RPATH. IMO, its best to use neither DT_RPATH nor DT_RUNPATH in shipped binaries.
unless
you ship all your dependent libraries with your executables and wish to ensure that things JustWork(tm) after installation, in this case use DT_RPATH.