I think one advantage is you can directly appeal a court ruling. To challenge an administrative order you need to sue the government. In some cases, you need to sue the government in a separate trial first, in order to get permission to start suing them for cause in another one.
Another advantage as the other reply has mentioned is that courts have broad authority but must narrow the effect of their rulings to the minimum necessary to address the suit. In this case it would certainly lead to 4Chan being blocked by UK ISPs by order of a UK court. I think even 4Chan would be fine with that.
They also force ISPs to block IPs [0].
I feel trying to say that's not "blocking websites" is playing games with words, and the results are functionally the same to the "average" user.
The fact that the US effectively claim juristiction over the root DNS system is a more a geopolitical power thing rather than a legal restriction.
[0] https://torrentfreak.com/us-court-orders-every-isp-in-the-un...