sport mode only allows the valves to open to 70%If you hit the Sport button, the valves are always open. Your car will always start in V8 mode, all the time. 4 cyl mode is only to help highway MPG. The 6.4s have a way better exhaust manifold, that could be the difference in the sound.
and to answer ops question yes installing an active exhaust delete kit will give you the cold start sound at all times.