Totally different players. Hewitt was a counter-puncher much more suited on faster surfaces while Courier was a rather prototypical baseliner suited for slower surfaces. Yes he had success on the faster surfaces, but he was a different player.
Courier would easily handle Hewitt in Australia and Roland Garros, however, I think Hewitt would beat Courier at Wimbledon/US Open, however, those matches would be a lot closer.
I wouldnt say Couriers game was that suited for slower surfaces. It´s easy to say that because of the two RG´s titles, but he definitely wasn´t like the clay court grinders of that era. He hit relatively flat, and he was much more succesful on hard courts. Excluding the two RG-titles, he only won three other titles on clay.
Courier's record at Wimbledon is still notably worse than Hewitt's even if you don't give Lleyton's win as much value. Courier made like one 4th round (which was his last Wimbledon), a QF and a final while Hewitt had four 4th rounds, three QFs, one SF and obviously the win. Lleyton also had the better record in New York as well by quite a stretch.
You have to remember that Courier made it to the WImbledon final in an era where he had to play against serve/volley-players like Sampras, Becker, Ivanisevic, Krajicek, Edberg etc, when they were at their prime, and grass was actually fast. That´s quite an accomplishment. Hewitt as a counterpuncher enjoyed playing in an era where the best serve/vollyers were already retiring and grass was getting slower. If prime Courier and prime Hewitt played against each other on fast hc or grass, i´d give Courier the edge, because he was the more active one of the two.