Ten Hag is as much the opposite of Alonso as he could be, there are literally zero similarities between the two coaches. I think it is a mistake, but who knows maybe it is owed to the fact that not too many coaches are available at all.
I assume that both coaches have different playing styles, but this is something that the Germans can control. I think they will realize if the direction Ten Hag is going to take them is the right one or not, especially when the team Knows that they are very good and that they have already won their own Bundesliga. In addition, what Xabi Alonso left behind is not just any old thing, he left the bar very high, it is a very strong challenge for an ETH.
I wasn't so much referring to the style that each coach wants their team to play, I was referring to the attitudes these coaches bring to the table and how they try to establish connections with the team as a whole, but also individually with every player. Alonso is not someone who leaves you alone with your issues or attacks you in public, he has the team in mind and always tries to unite them and have have everyone on board and work their ways towards the same direction. Ten Hag can't refrain from attacks and defamation. It's wired into his brain. Those coaches usually don't stay very long with the same team, see Thomas Tuchel. One of the worst human beings in the business.