TL/DR Blavatnik donated $6,390,683.36 more to Republicans for the 2016 election, $2.5 million to Moscow Mitch and $840K to Leningrad Lindsey.
Unfortunately, election donations are very opaque, so I decided to download the FEC data file, google the PAC names, then catalogue D/R to see who he was giving too. Blavatnik changed his donation pattern after the Dallas Morning News exposed him. Prior to the DMN article, his smaller personal donations went to both parties. The huge donations he was making exclusively to GOP super pacs were from his companies.
Looking at the 2016 election, his personal donations to both parties are intentionally obscuring the staggering imbalance in his overall donations when considering his companies. He personally donated a slightly larger amount to Democrats, but those donations are absolutely dwarfed by the money he donated to the GOP from his two companies.
In the 2015-2016 election cycle, Blavatnik personally donated $536,216.64 to Democrats (notably $40K to Michael Bennet, $20K to Kamala Harris) and $426,900.00 to Republicans ($40K to Leningrad Lindsey). That's +$109,316.64 to Democrats.
Now let's take a look at the companies Blavatnik owns that were mentioned in the Dallas Morning News article, Access Industries and AI Altep Holdings.
https://www.opensecrets.org/donor-lookup/results?name=Access+Industries&cycle=&state=&zip=&employ=&cand=
Total Access Industries 2015-2016 donations $5,500,000 (All to GOP with $1,500,000 to Moscow Mitch and $800,000 to Leningrad Lindsey)
https://www.opensecrets.org/donor-lookup/results?name=AI+Altep+Holdings&cycle=&state=&zip=&employ=&cand=
Total Al Altep Holdings 2015-2016 donations $1,000,000 (All to Moscow Mitch)
Total 2015-2016 donations from Blavatnik through his companies $6,500,000 (All to GOP). His biggest corporate donations were to Moscow Mitch, Marco Rubio, Scott Walker and Leningrad Lindsey.
Subtract $109,316.64 from $6,500,000 and it leaves a net balance of $6,390,683.36 more donated to the GOP than Democrats for the 2016 election cycle. That's not counting the additional $1,000,000 he donated to Trump's inauguration. Blavatnik used Al Altep Holdings to donate a further $1,000,000 to McConnell in 2017 before the DMN article was published.
His donation pattern changed after the Dallas Morning News exposed him using his companies to donate huge sums to the GOP. Since the article came out, he only has a single company donation, $100,000 to the Democratic Senate Majority Pac, the only donation he has ever used his companies to make to a Democratic candidate or PAC. The large donations to the DNC on his personal donations list are from 2019, well after he was exposed and is now trying to change the narrative.