Cases are typically assigned base on availability. However the Chief Judge can take any case he chooses. Since Chief Judges are most often the most experience judges they often take high profile cases.
Boasberg is known as one of the least partisan judges on the federal bench and has had favorable ruling in cases involving the president, for example his lenient punishments of Jan 6th rioter. And in Trump’s first term, he released FISA court materials that
exposed huge problems with the FBI’s probe into connections between Trump’s 2016 campaign and Russia’s election meddling. He also paved the way for conservative groups to obtain some of Hillary Clinton’s emails from her private server. Republicans were praising him and democrats were questioning his objectivity.
The head of the local bar association describe him as "A judge you knew when you went into court with him, that he was going to follow the rules. He is very predictable because he followed the law. He is not a rash judge at all."
Of all head judges, he has one the lowest rates of overturned cases.