Another (simplistic) explanation for why they are better at messaging is that for the last 20+ years (correlating closely with the rise of Fox News) is that the Republicans are much more comfortable telling outright lies. Not that Democrats are perfect angels, but so many Republicans feel that the truth is what is delivered by god/their leaders/their media that they have no qualms about repeating it. They don't even accept that logic, reasoning, or facts matter.

This is a radical departure from the past. I can remember political debates in the Reagan era. Both sides agreed with the facts, they just disagreed whehter the government should do anything about unemployment, or the debt, or the AIDS pandemic. Now, the Republican party has no qualms about ignoring facts, or making up their own "alternative" facts.

Reality is messy. The truth is messy. Lies can be simple, and thus easier to mess-age.