Short answer
Not simply. In matched 2020 US Senate races, Republican posts drew more engagement each, but Democrats posted about twice as often, so totals did not clearly differ. In Europe the biggest Facebook premium went to populists, and the very largest to the populist radical left.
What the evidence shows
- In 20 contested 2020 US Senate races, Republican posts drew about 50% more shares and comments each within races, though the strength of the evidence depends on how posts and pages are weighted.
- Democrats posted more (median 30 against 19 posts a week), and per follower Democratic pages drew, if anything, more engagement.
- Democratic posts drew a higher share of 'love' reactions in 17 of 20 races; Republican posts more 'haha'.
- In 17 European countries, populist radical left parties had a premium of about 5.4 times, against about 2.3 times for the populist radical right. Far-left parties that are not populist had none.
Caveats
These are patterns on candidates' and parties' own pages. They say nothing directly about Facebook's ranking algorithm or what ordinary users saw in their feeds.