Overall, IMO, Klopp is better than Ten Haag, we really can't judge MU success in winning the match against Liverpool as Ten Haag overall success in the EPL. However, in Liverpool history, Klopp has given Liverpool the important title they have always wanted, the EPL Trophy. Meanwhile, Ten Haag still hasn't been able to prove the effectiveness of his strategy in the EPL so far. I'm not saying Ten Haag is very bad, but it's not right to compare him with Klopp, who has been at Liverpool for several seasons. And we can't blame Klopp for losing results against MU, even Liverpool losing their 1st position.
It’s not even a debate, Klopp already has a title to his name this season so losing a match to Ten Hag doesn’t justify that Ten Hag is a better coach than Klopp. Ten Hag has achieved nothing for Manchester United since his arrival and he is barely making it to the top 4, he even got eliminated in the Champions League this season and they are having a very inconsistent performance this season which proves how terrible of job he is doing at United.
Klopp have achieved alot for Liverpool so far and it would be difficult for the club to forget all he has done for them, i think they are lucky to have him and he will be missed when he leaves the club. He has won a trophy already this season and he is currently challenging for the premier league title and also one of the favorites to win the Europa League title if all things goes well till the end of the season so there is no way you can compare both managers and decide that the winner of the tie between them is the better coach. Their performance as a coach should be judged based on the success achieved throughout the whole season.