I have played fewer courses by either Nickalus or Fazio than many here:
Nicklaus: Monte Rei, Portugal; Montecastillo, Jerez; Grand Cypress New, Orlando:, Eldorado (pre-changes), Cabo Ocean, Palmilla, all Cabo;
Fazio: Pelican Hill, Newport Beach; Primm Valley, Nevada; Raptor Grayhawk, Scottsdale; Sandy Lane Green Monkey, Barbados; Grand del Mar, San Diego
I like Nicklaus courses, and thought Monte Rei in particular, was terrific. OK, they are grand courses built with lots of nice of unimaginative features, but I remember some of the holes well. Likewise Montecastillo and Eldorado. I was much less impressed with Grand Cypress which I struggled to remember even shortly after finishing. Some of the themes of Nicklaus courses work for me - downhill shots to levels, few shots at the horizon, good framing with bunker, WYSIWYG.
The Fazio courses are also an interesting bunch. I loved Green Monkey, but I don't know how much of that was the spectacular setting and wonderful condition. Would any decent architect have done just as well with that canvas and budget? I really like Grand del Mar (formerly Meadows del Mar) and enjoyed Pelican Hill and Primm at the time although I don't remember those courses very well.
I think a lot of the sniffiness about Nicklaus, in particular, is a bit unfair. It seems to me that he is hired to give a reliably decent course with a big name cachet, and that is what he does. Perhaps it is a bit like eating in a reliable safe bet chain restaurant rather than a smaller, riskier but possibly more rewarding bistro in a quiet street. Nothing wrong with either one at the right time.