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The main "problem" is that the Hellcat uses a different supercharger - a Whipple - than the F-Type R which uses an Eaton TVS R1900.
The Whipple is inherently a noisy/whiny supercharger while the Eaton TVS was specifically designed to be quiet.
I'm sure a whipple is louder but I had a TVS on my 14' Lotus Evora S and with a aftermarket ITG cold air intake that deleted the factory airbox the supercharger whine was excessive to say the least as the intake hose was right behind the drivers window.