I disagree, the difference will be negligible. UHP winter tyres like ContiWinterContacts will be excellent regardless of width.
I'd personally go with the staggered set as it will provide more traction on cold, damp roads, which is a much more likely scenario. £100 is peanuts when you're buying 4x 18" winters.
Why does the vehicle manufacturer recommend 4 identically sized tyres for winter use then? Do they just do it for a laugh?