To answer this question, you first must ask "What are the elements of the Old Course?" My recollections of 2 fantastic years wandering past the Dunvegan Hotel to the 1st tee starters box are
1) Always asking which direction is the wind blowing? This influences the strategy on every single shot, and ensures that from day to day the golf course is quite different
2) On each tee asking where is the pin today? Beacuse of the multiple driving lines on each hole (generally many more than simply 'one side of the fairway or the other') you have to ask where is the pin to decide where is the best line from which to attack the pin
3)Once a driving line is decided you then have to take the wind back into account for the shape of tee-shot, and of course, the same applies for the approach- floater or bump'n'run (generally), where do i want to land the ball
4)If the green is missed, you then have a myriad of options to chip or pitch or punch or putt. Using slopes, or avoiding them.
5)Other important elements are of course the openness and 'crowded' feeling of the course, and of course the going away and returning to the town. However these can't really be compared with many other courses outside of Scotland (Moray, Carnoustie etc.)
Basically you are always given choices and challenged 'What is the best way to get my ball to the hole' and not only 'on what line to the hole' but also 'what way...ground or air'. On tight, target golf courses, the course dictates the best way to the hole, and if you don't do that, there is rarely any recovery. That is another great aspect of the Old Course, you rarely have to give up the hole (as long as you avoid the pots). The key is that imagination is highly rewarded at TOC, but not at many modern courses.
To answer the question, in my experience I would say Royal Melbourne offers the wind and many of the same strategic choices (width, variety of approaches, short game variety), the Ocean Course at Kiawah may not offer as many bump'n'run and open approaches, but certainly offers the openness, the wind and quite a bit of width/decision making. I always thought the old Augusta used to feature similar traits. It was a course both Nick Faldo and Seve Ballesteros could win on. I'm not sure Seve or Sergio could ever win at the new Augusta- there is simply not enough room for imagination.
I know there are many others, i even thought i detected hints of it at the Old White Course at the Greenbrier, i found myself with different options on some of the holes. CB MacDonalsd early influence i suspect, but much of it has been lost.
Greg Ramsay
www.barnbougledunes.com