I'm aware of Perl exceptions and how to handle them. What I do with $@ is really not germane to the question, which is to determine if there is any functional difference between Module::Load and eval "require $module"
Your code uses the same general approach as Module::Load (albeit expressed more succinctly) namely to create a filename out of a module name and pass that to require.
So, other than style, is there any technical reason to choose this method over
eval "require $module";
die $@ if $@;