The recoil characteristics differ. The recoil of the shotgun increases slowly to the peak. The recoil of the .308 bolt action develops faster and is more pronounced. I´d join benjammin´s rating. I rate it roughly at half or a little less. The .308 was an old Steyr SSG and my 12 ga shotgun is an over and under shotgun made by Mauser. The shotgun is a light weight hunting model.
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If it isn´t broken, it doesn´t have enough features yet.