So, blood purity is, presumably, totally uncorrelated to anything in the harry potter universe.
However, in a weird statistical quirk, that should mean that, within Slyhtherin, pure-bloods are systematically less cunning or ambitious than half-bloods. Why? Because the hat presumably wants to balance houses. So if you have a pure-blood, this makes them more suited for Slytherin, thus meaning they require fewer other characteristics. And conversely, a half-blood would have to be more cunning to clear the bar.
And amusingly, it also means that outside of Slytherin, being a pure-blood should be positively correlated with the attributes of the respective house. This is true by symmetry, but you can also see it logically; if you're a pure-blood, you have an easy ticket to Slytherin, so if you're not in Slytherin, it's a sign that your qualification for another house is strong enough to outweigh that.