I've never been to a Fazio course, so cannot comment, but I have seen Nicklaus's 3 signature courses in the UK, and played two of them: Carden Park, The London, St Mellion.
Carden Park is about 30 miles from where I live. It is featureless. There are a couple of holes on which there are strategic options, and the obligatory lake holes, but I'd rather play Portal (Donald Steel) or Mottram Hall (Dave Thomas) if I had to pick a modern course locally.
The London Club has two courses, one a Nicklaus signature course, the other by his company, unsigned, as it were. This one I've not played, but I was given a hole-by-hole tour of both courses by a member of staff. They're in gently rolling country south-east of London close to Brands Hatch motor racing circuit. Again, my impression was of something rather featureless - I had to find something positive to write about the courses and maybe I would have found more had I played the courses, but somehow I doubt it. I have the course planners to hand yet remember almost nothing about them.
I loved St Mellion in Cornwall. True, there are a few bland holes up on the level ground by the clubhouse, but the holes in both valleys had real character and quite a lot of originality. I was then playing about 50 shots a round better than I am now (ie a 50-50 chance of breaking 100) and I found myself relishing the prospect of so man y of the tasks set. On the same trip I played West Cornwall, St Enodoc, Trevose, Lanhydrock, Thurlestone, Yelverton, Manor House Hotel, Westward Ho and Saunton so I had a good set of yardsticks by which to judge it. It's probable that Mike Clayton has played this one on tour and would probably come up with a very different assessment, but from my amateur viewpoint it's a course on which the holes have remained clearly etched in the mind quite some years later. Nicklaus is said to have reckoned this to be one of his better efforts.