Mike
in 1999 we restored the old second hole at Greate Bay , in Somers Point , NJ ( Park 1923. with some renovations )
In doing this we had to rip up a hole that Ron Garl had built for previous owners in the mid 1980's. Garl's renovation changed the starting par to
#1 par four (410)
#2 par 3 (185)
#3 par 4 (365)
#4 par 3 (125)
it really didn't work too well, with delays early in the round and Garl's renovation had replaced a really good tough four par with two average (at best ) short holes...in ripping up his 2nd hole I was concerned as to Mike C's question.. that the new green we now had to build would not react / putt like the other 17 existing holes.
We had enough room to flip the tee on the short # 2 and make it the 16th hole, which fits rather neatly into the routing, and in the process improved the course by restoring one of Park's original holes ... which is now our second hole and one of the better holes in the area.
Our course now starts par four , par four , par three and pace of play is much improved, an added bonus.
Back to the new green on now #16 and how it relates to your question.
We striipped the sod off the green...stored it in a hothouse for two days and returfed the new #16 green with it.. in December no less.. and had it fully operational by June 15th . After building it more or less to USGA specs.it requires slightly different care, as expected, but I would defy anyone who didn't know that we did this to identify it as different from our other greens today.
In our case we got lucky, and established a green that plays , looks , and feels like the 1923 push up originals!
So , for my money, it's the turf, not the construction method that changes everything. Our experiences, a new green that most closely resembles the original ones, is an interesting success story.