Doesn't matter what length with no hearing protection they will both damage your hearing severely. My advice to all new and old hunters alike is to suppress the rifles you hunt with. Suppressors are cheap, light and effective.
To the subject matter. If it's a 30-06 like your example and you intend to shorten it. Sell it, buy a .308. Cut it to 16", not 18". Put a DPT suppressor on it. 4" forward means it'll handle like a 20" barrel.
Regarding sound we have as regular hunting rifles a 22" 6.5PRC and 22" .270win and two 16" 308win. All with DPT suppressors. The 308s are considerably louder than both the .270 and 6.5PRC (way more powder than 308 but 6" more barrel). The .308s still don't make your ears ring and seem quite tolerable to unprotected ears - I suspect they still damage hearing but several orders of magnitude less than unsuppressed.
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