Can't help you with the match play as I've never seen the UoM GC. I probably have played Scarlet over 500 times, but only once since the Nicklaus renovation.
I can tell you that during my time in Columbus, the Michigan course was not considered in the same light as its football team. People I knew who played it thought it was a short, fun course, far from being of championship quality. This is probably reflected in the number of Div. I NCAA championships hosted there: one to Scarlet's 10.
Scarlet suffers from four or five things. 1) it is a very demanding course even when it was under 7200 yards before the Nicklaus renovation; 2) conditioning was well below that of the private courses in the area as it is (or was when I was a student there) maintained by the Maintenance Dept. of the university and the approach seemed similar to that in taking care of buildings, green areas, and other infrastructure- tired and rough around the edges; 3) the golf operations are/were led by the Athletic Dept. and the approach was military in nature and at times adversarial with staff, maintenance, and students; 4) similar to Long Island, it is compared with some outstanding, well-maintained, lightly played private clubs (MV, Scioto, Golf Club, Double Eagle) nearby; 5) it is not a particularly attractive course, bounded on three sides by busy four-lane city streets.
Re: the Nicklaus renovation, based on reports from people on this site, I hadn't made a point to see the course since a visit when it was being cleared and much of the rough shaping had been finished. My expectations, admittedly, were low, but I think that the removal of hundreds of trash trees greatly improved the course. I didn't find the bunkers too deep or penal, nor the addition of back tees a problem- I played it around 6800+ yards and it felt pretty much like the old Scarlet, though with wider vistas and freedom of play.
I found that the biggest complaint, the re-routing of the last third of the par 5 #4, to be without merit. Though it did create a walk-back to the tee for #5, a strong par 3, the original green site with its bunkering scheme and often poor condition due to its sheltered location, made this one of the lesser holes IMO. The Nicklaus re-siting of the green makes for a more demanding lay-up and approach shots, bringing in part of the lake into play. There is typically a wait for the fifth green to clear, so the longer walk-back, leaving the bag halfway to the green, does not interrupt the routing or the flow of the round.
IMO, Scarlet is a vastly underrated course. Would it not be for the way it is operated and the heavy use, I'd be happy finishing my playing days there.
Oh, and the football appears to be pretty good too!