-snip-but 80% of the style and strategy of play applied by a coach will remain the same even if he coaches different clubs.
Some people think Manchester United has an advantage because Ten Hag was once Ajax's coach so he knows how Ajax plays. But this also provides benefits for Ajax and that's exactly what you say. Ajax still has several assistant coaches who once helped Ten Hag at Ajax so they will be able to know the playing patterns that Ten Hag usually applies. Ajax can have different game tactics because they have different coaches and Ten Hag has been away from Ajax for 2 years. On the other hand, I think it is difficult for Ten Hag to change his training patterns and that will be his weakness when the two teams meet.