The first thing, I think, is mental strength and dedication. My club is littered with players who had shots at being pro and for whatever reason, passed it up. The constant training - the hours in the gym - the attention they have to pay to their nutrition - not everybody wants to live like that. There's plenty of people who'd rather be chasing tail, or smoking pot, or getting rich instead. Ultimately, a player has to want it badly and I don't think most people want it that badly.
The second thing is having the body for it. The pace, the strength, the size - they'll all fairly rare commodities and you see plenty of really promising schoolboy players fail to make it because they simply aren't good enough athletes. Not uncommon either to see talented players bulk up to find that last bit of athleticism needed and find their bodies can't hack it.
The third thing is consistency. Coaches hate players who are brilliant one game and poor the next two. There's no use to being able to land kicks from 60m if you only get one in ten, or throw perfect miss passes off both hands if half the time you do it ends up with the spectators. Also, not a lot of use being able to do a couple of things extremely well and most other things poorly. Props need to be able to run, fly-halves more and more need to know how to tackle, and so on.
Sadly, technical ability and mental ability comes after those three most of the time. Of course, you'll see tiny players with outstanding decision making and technical skills make it from time to time, but they are a rarity. There is a very conscious decision at a lot of academies to make rugby players out of athletes than the other way around. The NZ posters will no doubt pipe up with "Not here", which is true, but I suspect that's got more to do with not having to make the choice that often; there's no shortage of young men in NZ (and in other rugby strongholds) who are both.
But ultimately the big difference comes down to being willing to work like mad. That's how I see it from the outside anyway.