The rumour is that at Souths he treated a couple of players - Cody Walker and Lattrell Mitchell - with kid gloves, and they weren't being to the same standards as other players, with cliques emerging in the squad. Burgess apparently wanted them bringing into line and the row that developed led to him leaving. They've been awful this season under Demetriou, but Souths had allowed their roster to age badly, with a poor front row (sounds familiar...) and letting Adam Reynolds go being seen as really poor decisions.
Arthur was Ok at Parra I think but had probably just run his course. Not helped this year by injury to Moses, but they've taken a few hammerings and it looks as though the players had stopped listening.
Right now I'd say Demetriou would be higher risk, but who knows? Arthur would send a big message of intent at least.