The comparison with Rees is a bit off...
There are three similarities between Carr and Rees.
1) Rees could throw a reasonably good short range pass based on pure timing.
2) He was one of the best we had at making pass protection audibles, although sometimes he'd take way too long to make the call, and delay of game penalties were numerous. Carr doesn't take too long.
3) He was good at sliding around in the pocket, buying a second or two more to find the open short range receiver.
That's where the similarities come to a screeching halt.
CJ Carr is decently mobile. He can scramble for decent yards, and can actually move the pile forward. No, he won't run a 4.50 in the 40, but he's not going to run it in 5.25 either.
Tommy Rees was easily the slowest QB we have ever had in modern Notre Dame history, along with having the weakest arm. To put it this way, Drew Pyne looked fast and strong-armed compared to Rees.
During some cases where he got completely flushed out of the pocket, and had a lane open to run, his acceleration was so slow, that by the time he got close to the line of scrimmage, the defender would drop him for a loss. Anyone else would have easily made at least the line of scrimmage and gotten positive yards.
The offensive lines weren't to blame. He had several studs blocking for him.
Michael Floyd, and later, TJ Jones, bailed him out of numerous really bad throws.
Opposing defenses neutralized our offense by simply rushing only three, and dropping 8 into a very short zone coverage. They knew he was zero threat to run, and couldn't throw a reliable ball past short ranges.
The fact that even in Rees' physical prime, he couldn't outrun a police officer who wasn't exactly athletic, wearing 20 lbs of gear on a duty belt with really bad ergonomics, and had to resort to a kick in the junk, tells you how lead footed he was.
Carr can make all of the throws, with good zip, accuracy, and timing. He can also read receivers breaking open faster than anyone else we've had, with maybe the exception of Jimmy Clausen.