After having read the first 5 chapters here's my thoughts ...

1. Whatever it's going to do it definitely isn't going to succeed Naruto ...

2. Aside from the common "hard work pays off" which is in almost every battle manga geared towards the shounen demographic, I've seen not a lick of anything else that would hint a tragic sub-plot or a dark and serious story ... 

3. Well if the themes are "staunchly different" then it most certainly isn't comparable to Naruto in any way and I doubt any other new themes that would be comparable to those in Naruto will develop when the the sample of what I tried and the title "Boku no Hero Academia" are anything to go by ... 

So far Boku no Hero Academia is a far cry when it comes to the concept and the qualities of the themes that Naruto had. It feels nowhere near as good as Naruto is. The closest thing to Naruto that's also serialized by Weekly Shounen Jump right now is World Trigger and that's stretching it ...

I'm really confident in what Kishimoto's next goal is! His one-shot, Mario, was fantastic read in my opinion. Based on how Naruto changed from its one-shot, I know that taking the time to create what he wants will pay off. I know he said, during Naruto he had ideas for a sci-fi manga, so that might be what he goes next. 

I know what you mean when you draw in value of Naruto compared to the others you mentioned. Even with One Piece, my favorite of all time, I may have never been fully redrawn into it if it was not for Naruto (4Kids those days). It's also like I said before,  Naruto was indeed the driving force for many anime viewers today in the western world and many have also diverged in their preferences since. For something like to be a driving force to you like Naruto was isn't really ever going to happen. Though I can't see anything doing that for you or anyone who grew up with Naruto in that way. That's part of what I meant by Naruto isn't replaceable.

Boku No Hero comes at time that's much harder to get the same popularity as Naruto with a western audience. I also don't think its going to blow u over night like Attack on Titan. However, I really feel that it will have much of its longeivity and impact with what probabably is a smaller scale. I think that's fine because the Wetstern world has has been more acclimated to anime than it has ever been. I've really just been reading and really thinking about the lengths it can really go.

I agree about the nme adjustment among other things. I hope that they wait for a long time before starting the anime and pace it properly, as well as get a great studio like Madhouse.

I think it's very difficult to tell what will succeed Naruto or any of the big three. You just can't tell what will stick with the western audience. It just happens. Shows like Attack on Titan and Sword Art Online made big impacts, but unfortunately those aren't continuous series in their original medium from which they are adapted. The best thing to do is wait and watch. I'm sure we'll eventually get something that's big over here. But to me it doesn't matter because I already get to try out all the niche and super interesting stuff every season since anime and manga have become pretty popular entertainment over here. I just hope for something big to come along so more people can be introduced to the fun.

Hard to compare Boku no Hero with finished mangas. Since its still in its early stage, I think we should try to compare it to the first arc of Naruto, DBZ, One Piece, Bleach or any other mainstream animes. I can say judging from it's popularity, theme, and current chapters. This Boku no Hero has the potential to be part of the "mainstream" category. Can't wait for its anime! It's already confirm that it will be animated soon. A bit too soon than expected but that's okay with me.

I was considering reading it until I found out that they're working on the anime which I guess i'll just wait on.

What its already been announced? I haven't read it for a couple of weeks so I was none the wiser. Ugh, way too soon.

I started watching One Piece about a month ago. I managed to watch 4 episodes and I seriously don't get its appeal. Does it get better? Did it start rough or something? It looks like a cheap imitation of other anime I've watched. I am aware it was made long before the ones I have in mind, but still.

Naruto has been one of the best anime I've seen (comes right after Death Note which was slightly better). The latest fillers of Naruto have been beyond annoying, but if you take those out and watch it twice a year in a bulk, it's still amazing. Sure the Pain Saga was awesome, but the ones that followed were also good.

I don't see Boku no Hero Academia having the same appeal, but Attack on Titan has been huge and it's a really good anime.

One Piece is easily my favorite shonen action manga...but I also don't really care for the anime. I tried it a few times, and it never seems to hit the right note with me. The pacing seemed slow, some poignant scenes are censored, and I'm not a fan of the animation quality or OST (though that's subjective obviously). It seems to me like a series that shines much brighter in the original medium.

That being said, the series definitely does get better as it goes on. I wasn't completely hooked until the Arlong Park arc, which is the fourth/fifth story arc in the series. Oda's story-telling abilities improve as it goes on, and some of the later story arcs get suprisingly heavy. I'd say it's definitely worth watching more if you're interested in shonen series. 

One Piece starts off slow in comparison, but really hits its stride as time goes on. Basically like Super_Boom said.

Also One Piece as an anime is especially slow. This is mainly because one chapter = 1 episode as opposed to Naruto where its 2-3 chapters.

A lifetime ago, I watched it on 4Kids, when I tried going back to it subbed years later I ended up just going to the manga until major arcs like Arlong Park and Enies Lobby

Wow your intro was beautiful. You are 100% right people may have really criticized Naruto hard but from chapter 1 it stuck with what it introduced and growing up with Naruto personally was one heck of a ride. As for Boku no Hero i'm on and off of reading it not because there is a problem with it just because I really just wanna read it straight through instead of having to wait for it. As for being Naruto successor...It can happen, but not yet.