The compelling part about Matthäus, and the reason why he is held in such high esteem as a mainstay in a myriad All-Time XIs, is that he could do a bit of everything, and mastered different aspects of midfield play over his long and illustrious career. In a defensive sense, he was extremely dogged when the situation called for it and he got specific instructions from the coaches — for example, consider his man-making job on Maradona in the 1986 or 1990 World Cup finals, particularly the former as Diego was at the peak of his powers. From the heart of the pitch, he could pass and move...and dribble just about as well as any other central midfielder in football history, often like a hot knife through butter with regard to penetrative potential. His end-product as an offensive threat was substantial, even as a young player with Mönchengladbach — and overall, he boasted a comparable goals-per-game ratio in league matches to someone like Lampard (who is exalted for his productivity):
And of course, his mentality and grit and determination-to-win was supreme. As good as Keane was (favorite United player growing up for what it's worth), he didn't quite match Matthäus in terms of the comprehensiveness of his skill set. And of course, Makelélé was even more of a specialist at his pomp. Matthäus was very unique...a real one-man-army, like a more accomplished and long-lasting version of Robson (one of the few central midfielders to come close to him in terms of completeness of play).
Additionally, he is proven in what was the greatest and most intense league period in football history, late '80s to early '90s Serie A — which boosts his profile to a considerable degree. Just to sample Matthäus' competition, Milan had van Basten, Gullit, Baresi with Sacchi at the helm, Napoli had Maradona, Careca, Ferrera and so forth, even members of the non traditional-elite like Sampdoria, Hellas Verona or Fiorentina boasted the talents of Baggio, Mancini, Vialli, Elkjær, et cetera. And he delivered a title for Internazionale after a decade-long dry spell, while bearing the burden of being of their #10 (i.e. the primary inspiration in midfield and attack).
When you take wide-ranging talent and unending list of accomplishments into account, he trails only Beckenbauer and Gerd Müller for German footballers — which says something because they also produced Rummenigge, Breitner, Seeler, Walter, Sammer, Lahm and so forth.