Interesting question. I know a lot of people talk about gentle handshake to get started and I can see the appeal of that, but the ones I like are generally not that easy. Since I was just playing them both, I would pitch the 1st at Royal St George's and at Royal Cinque Ports. Played RSG in a howling gale in the Hewitt a couple of weeks ago (solid 45-50mph wind). Drove it past the fairway bunker (never done that before) and my partner couldn't hold the green from 75 yards away straight down the wind. Conversely if you play into the wind, it's a good drive to get over the kitchen and then you've got a mid to long iron to a green hidden behind a bank of bunkers. The nice thing about this hole, at least in the conditions I typically play it is you can hit it virtually anywhere and you'll find it and have a shot.
RCP is a lot more fun to watch others playing than it is to play. With the wind into and off the left, the clubhouse looms very large. I've seen plenty of people closer to the 18th green than the 1st fairway as a result. Then if you miss the fairway you've got the "do I don't I" decision to make.
This side of the pond, close to me in the not gentle handshake is Bethpage Red. 470 yards with a semi blind approach up a hill. Extremely hard four. It's going to be extremely hard whether it's the 1st or somewhere else in the round, so I don't think it loses much in that regard. It's a 4.5 hole, so whether it's got a 4 or a 5 in the par box on the card shouldn't affect your opinion of how to play it.
One thing all of these have in common is no OOB close by. I'm not a big fan of an opening hole with out of bounds in play. I want to know which way it's going before I have to contend with holes like that.