They've just come into being in Bolton and Wigan GM boroughs, my neck of the woods, and thus far the difference is they're wrapped in yellow. I'm very happy with the change though - the aim is that bus, train and Metrolink is integrated, with a single tap in/out system like Oyster in that London. Fares are also easier and capped, rather than it becoming dear if you're changing busses between different companies.
I think real change will be noticed if bus frequency and/or more, better routes are put in with subsidy, where private firms wouldn't take the profitability. There are loads of services on the periphery of Greater Manchester that are hourly where every half hour would be far easier to use.
If Liverpool can get it set up to work with bus and Merseyrail combined to lower fares it should be worth it.