What personality differences are there between registered Democrats and registered Republicans?
Studies have found differences in the psychologies and habits of liberals and conservatives. I found one convenient webpage linking to a number of these studies. There is also a Scientific American Article discussing some of these differences, and Google turns up tens of thousands of results on the subject.
While there are some oddities (e.g. conservatives tend to dream more mundanely and remember their dreams with less frequency), many findings are unsurprising, and some are almost tautological, finding that conservatives hold conservative values and liberals hold liberal values. For example, conservatives emphasis cleanliness and purity more than liberals, and while conservatives are more focused on preventing negative outcomes, liberals are more focused on causing positive outcomes.
"Systematic" may be too strong a word. While conservatism and liberalism correlate with these personality traits, they don't necessitate those personality traits. We should also be careful not to confuse correlation with causation: just because certain personality traits may be correlated with liberalism or conservatism does not imply that those personality traits cause or are caused by liberalism or conservatism. Nevertheless, personality is, to some extend, a predictor of political ideology.