They seem to do the same thing.
$c->reply->exception('foo');
return;
vs
die "foo\n";
Should I chose one over the other?
The latter is easier to read, can be trapped at the appropriate level if needed, and can include stack traces and context in development mode via automatic Mojo::Exception wrapping. It also will act appropriately in a promise handler or async sub, causing the promise to be rejected.
You can see exactly how it's handled here ($next->() is the call to the dispatch chain): https://metacpan.org/source/SRI/Mojolicious-8.33/lib/Mojolicious.pm#L208-214