"Do you believe most Westerners today possess more Giant or Turanian blood?"
It seems genetic studies suggest Westerners have much more Turanian blood than Giant blood. However, a word of caution is that these studies are measuring the overall amount of DNA--which is mostly just junk DNA.
In terms of phenotype, physical anthropologists in the pre-DNA days certainly saw a strong continuity between ancient Paleolithic skull morphology and present-day Westerners. So, perhaps there is more Turanian (and Neolithic) junk DNA in Europe, but it would be difficult to examine only the genes encoding for personality traits and other characteristics to make a determination as to whether Turanian or Giant traits have more prevalence.
https://www.nature.com/articles/nature14317Another warning is that the proportion of blood probably varies greatly between individuals--perhaps some individuals today have almost completely Paleolithic ancestry, but if the graphs are averaged out over an entire population, this might get drowned out.
(I would give an additional warning that just because the Sardinians are the modern group with the most Neolithic ancestry on the chart, this doesn't necessary mean they are more noble than the other populations. Apparently herding has been a major part of their economy there for many generations. So, even if they inherited most of their junk DNA from Neolithic farming ancestors 5,000+ years ago, doesn't mean they continued the same lifestyle and attitudes into the present.)