The difference is often referred to as 'voice vs. exit'. You have a 'voice' (your say/vote) with the government, but no right to 'exit'. In contrast, with a private party, you only have a right not to transact with them (exit), but no right to tell them what to do (voice).
Your desired scope of government usually reflects how much you believe in exit and voice. For practical purposes, this usually translates to how efficient you think competition is, and how effective you think democracy is.