Benefit: The Internet is a cheap wide area network.
Risk: Cheap doesn't mean secure.
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Benefit: The Internet supports "convergence" -- so email, file transfers, VOIP, central database access, etc all go over the same pipe.
Risk: Everything on every client and every server is (potentially) available to anyone!!
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So....pick the benefit which you want -- but recognise the risks. Clearly for the NHS -- CHEAP trumps RISK (no pun intended)