In my opinion, much of the market is just trying to guess where the US will go (obviously with exceptions - sometimes Europe is more directly important). Our advantage is that we get hints from Asia, but we largely share the market movements with European exchanges. Look at London right now. Hardly down, so we're just mirroring what they do. So...what advantage do we have over e.g. London or Germany? None, I'd say. Asia yes, because they're often flying blind on a Monday without any cues from other markets.
I think US has the influence 24/5, either directly or through their futures markets, although Simon says that Europe is where the action is until the US opens because that's where the volume is. Either way, the US futures and Eu markets track each other closely in terms of movement (not level). US open only hints at what they'll do later, and often leads you astray. They don't want you knowing exactly what they'll do, so they often hide their moves until later. Often the big stuff happens just after Europe closes, or at the US close. Remember - they're always trying to trick you, and "they" is often a computer.