If you want go to the East coast though, you might find Brisbane to be friendlier to the right than Sydney or Melbourne. However, Sydney is okay as it's more of a middle ground in terms of political disposition; Melbourne is probably the most left-leaning of all, although it's less left-leaning than most US cities. It's not impossible to find a right-leaning community in either Sydney or Melbourne, but they're much harder to find and leftist communities are much more prominent in both cities.

Between Australia and the US, Australia is much more calmer, and as a Commonwealth nation governed by a common law system that up until 1986 had been tied to the UK, is more familiar to the British ex-pat. However, the downside is that it's subject to the whims of greater powers as it's a much smaller nation in terms of geopolitics, does not have an armed populace, and is also much less "exciting" since it's very peaceful. I can't attest to the US as I've never been there, but my feeling is that there is always more inherent opportunities in the US given the size and energy that it has, and how life there is inherently "riskier". If you do go to the US, I recommend a safe red state with a love for firearms.