Depends on if you think about it in Pokemon terms or in realistic terms, I think.
In Pokemon terms, it's hilariously easy to beat the E4 and Champion. A ten year old kid could do it, after all. Seems like all you need are powerful enough Pokemon and a spot in the hall of fame is yours. Assuming all of these 1000 trainers beat all the gyms already and are competent trainers, the majority of them would probably make it.
In realistic terms, the E4 and Champion are supposed to be the most powerful trainers in all the land. Are they really going to lose to some ten year old kid, even if he did somehow beat all the gyms? Heck, realistically, some kid probably couldn't even beat a single gym leader, because they would be professionals with advanced battle strategies and powerful Pokemon. And even if said trainer was powerful and could do all that, as previously mentioned, the E4 and Champion are the most powerful, so few of the trainers trying out could get a hall of fame spot. Maybe 100 out of the 1000 at most? Just my estimation.
As for how easy it is in each region, it depends on the strength of the E4 and Champion in each of those regions, I suppose. You'd have to look at their strengths in the canon, as that's all you have to go on. In Pokemon terms, Levels would be the best thing to look at, since that's all that seems to matter. However, in realistic terms, one would need to look at the kinds of Pokemon they use, their strategies, and even the kinds of moves they use to make an approximation of their power as trainers.