Highlands Links has benefited from very ambitious PR work in recent years, since the 1996 "restoration" by Graham Cooke/Steve Miller. That's at least partially why Highlands Links receives more press than Capilano these days.
Capilano's 6th and 14th greens (as well as, I think, the 11th) are Les Furber's work, Ran. And they're not very good. So the course might not be as close to original-Thompson as you think. Plus, the green surfaces there have shrunken significantly, and more than a few trees should be felled.
The front nine at Capilano is nowhere near as strong as the incoming holes, beginning with the par 3 ninth. Thirteen, and #14 thru #18 are also some of the best holes I know of. Still, Highlands Links is the better golf course; at least according to the "Morrissett Match-Play System":
#1: (Highlands Links) HL 1up
#2: (Highlands Links) HL 2up
#3: (Highlands Links) HL 3up
#4: (Highlands Links) HL 4up
#5: (Highlands Links) HL 5up
#6: (Highlands Links) HL 6up
#7: (Highlands Links) HL 7up
#8: (Highlands Links) HL 8up
#9: (Highlands Links) HL 7up
#10: (Capilano) HL 6up
#11: (Capilano) HL 5up
#12: (Capilano) HL 4up
#13: (Capilano) HL 3up
#14: (Capilano) HL 2up
#15: (Halved) HL 2up
#16: (Halved) HL 2up
#17: (Halved) HL 2up
#18: (Capilano) HL 1up
As you can see, Capilano gets much better as the round progresses. But still, I can't agree with Brad's opinion. Reversing the routing of the first nine holes doesn't make sense. First of all, the 9th doesn't return to the clubhouse. And, as Ran points out, playing the 5th and 6th uphill would be suicidal!