Obviously every architect puts a lot of work into the green design, and the good ones look at not only how the green will play but how the hole will play to each pin position.
I believe there are two types of world-class greens on the ends of the spectrum: those with multiple equal challenging pins and those with a large disparity between easy and hard.
Some examples: Easy-hard
AGNC #16, upper right vs. lower left. I'm sure that the hole plays over a half stroke tougher with the pin on the high right shelf. This makes it a hole that you must survive likely by playing below the hole and working hard for a two-putt. Alternatively, the lower pins can be attacked by using the slope of the green and most players have birdie chances. With these pins the hole can be attacked, and on Sunday it is the last great chance for players to make up ground or build a lead.
TOC #17, now I don't think anyone would ever argue there's an easy position on it, but back left (over the bunker) has to be considered much more difficult than the front pins. There are some exceptions, such as NGLA's road hole which has a bail area left and over the bunker, however I think the back left pin on the original road hole makes the hole play closer to a par 5, while the front pin makes it more of a par 4.
Pebble #17, Eh, it's not really that good of a green, and the least favorite of many on the course. Moving on...
Cypress Point, #9, I haven't played it, but I would consider pulling driver with a front right pin, never with back left. I hope others can chime in to help, on this one and on the others...
Interesting but equal (I'd list more, but I think this group needs more input from people who've played the hole):
Old Mac #5, I've only played it once, but it seems to me that no matter where the pin is you must keep it below the hole and not stray too far to either side. Favorite hole on the course, despite my 4-putt double from 25 ft.
If you can, please contribute to this list so we can get an idea of quality of the hole on both sides. Do you prefer one style to the other? Is there an obviously weaker pin position in the hard-easy category?