Just wanted to give you a Danish perspective to what kind of player you'll be getting in Højbjerg.
To be honest I think he's defensive qualities are highly overestimated, and his offensive qualities grossly underestimated. His leadership qualities are accurate. He is a leader type.
He was brought up at Bayern and given a chance under Guardiola. Would he really flourish in that clubs youth system under that coach, if his offensive passing abilities are as atrocious as the Saints forum seems to suggest?
On the other hand, he didn't lose his spot on the National team because of his lack of offensive capabilities. He lost it because of poor discipline when it came to defensive duties. As I recall he was subsequently dropped from the Southampton starting 11 around the same time as well.
But to his credit he seems to have listened to what his coaches told him, and he bounced back and became starting 11 for Southampton (and captain) as well as back in the National team (he usually play alongside Delaney from Dortmund with Eriksen in front of them in a diamond). What changed? He's much more professional and disciplined and works harder for the team. He doesn't try and play the Barcelona killer pass every time he gets the ball (he did that a lot on the National team) but plays more simple. Also, If you notice him during a game he always wants the ball. He never plays scared. He's never intimidated. And he IS better defensively than he was before - probably due to how Hasenhüttl plays with Southampton. But he is not a classic DM.
I still think though he's overly aggressive sometimes when trying to win the ball and can be quite slow in getting back into position if caught high up on the pitch. The flipside of those impressive ballwinning statistics he has is that he will not always intercept the ball in those mad rushes towards an opponent, often leaving a lot of space behind him and creating a dangerous situation for the opposition.
If you want someone to compare with, I think he's quite a similar player as Gravesen was when he played for you.