Arriva's operations in Liverpool, before they took over MTL, were a bit of a joke. They were competing on rat-runs with MTL on everything and had very few evening or Sunday services. Buying MTL was a no-brainer and a situation in which they couldn't really fail. After consolidating competing MTL/Arriva services and thoroughly renumbering the bonkers system inherited by the previous dominant operator, they've done alright but not anything particularly ground-breaking service-wise.
Their fleet renewal policies have been more interesting, huge investment in double deck buses in recent years obviously influenced by higher ridership and some of the newer hybrid technology has been innovative. The Arriva app is an excellent addition to anyone's smartphone.
The hive-off of Gillmoss to Glenvale, subsequently acquired by Stagecoach, was probably a good move. Both Arriva and Stagecoach, aside from their joint quality agreements on the 10/14/53/79/82/86 group of routes, seem to respect each other's "territory".
I can't judge Arriva's contribution to transport anywhere other than Merseyside, and it's good. But all at the expense of a genuine local ex-PTE operation that got into financial trouble.