I'd expect them to be close. In a two party system, the parties will coalesce around similar policies. The electorate will always have variance along the first

I'd expect them to be close. In a two party system, the parties will coalesce around similar policies. The electorate will always have variance along the first principal component (which probably corresponds to community prosperity vs individual comfort), and the parties will project in opposite directions, but nevertheless staying close to the centre.