This is the one... (very slight spoilers)
This is the Shonen anime you should be watching.
Forget "Naruto", since that is for all intents and purposes a rip-off of the manga "Hunter x Hunter" (the author more or less admits to it). The biggest problem is that "Naruto" actually did everything a lot worse, and that is the one that has skyrocketed into fame.
"Hunter x Hunter" has had a lot of problems. Extended down-times, due (most likely) to illness and Togashi having children, has made the release schedule sketchy at best.
If you can get past this, though, you'll be rewarded with one of the best mangas/animes you will ever see. Everything, from the characters to the world and the different powers, feels tight; well thought-out. If you're coming from "Naruto", you will most likely recognize just about everything in "Hunter x Hunter". The difference is that almost everything in "Hunter x Hunter" just feels more plausible. Things are still way over the top, no doubt, but everything the characters can learn and do, is connected to who they are as a person.
Nen (and its specializations) is the tightest, most water-proof power system I have seen in a manga/anime. It actually feels like something that could be true - far more so than any other fantasy shonen.
As for the main characters, they are well-rounded and genuinely interesting. There are few important characters who feel generic in any way. The main bad guys (Hisoka and The Phantom Troupe) are doing things for one or more actual reasons, and they're doing other things while not being able to pursue their main goal. They feel alive in a way that Akatsuki and Orochimaru, for instance, never do in Naruto.
The four main heroes are fun and cool, as well as genuinely thought-provoking and "alive". There is darkness, there is light. In all of them.
The best examples are probably Kurapika and Killua. These two guys were mashed-up and became Sasuke in "Naruto". The thing is, though, that Kishimoto completely missed the point of the characters. They are two people who are teetering on the very tip of a knife edge, but they came to it from different sides - that makes them so much more interesting than Sasuke, who just plunges headlong into darkness at the first possible chance.
As for the protagonist...
Well, Gon is Naruto, only much more likable. And smarter. And less of a goof. And someone who you can actually believe, leads by example. He is a character who you don't sit and wonder "Why the hell do people in the show even like this guy?" And, of course, since his power base is Nen, his powers reflect his personality. No massively overpowered techniques which can only be described through magic - training your body and your spirit gives you your powers. Full stop. Yes, there is the "Aura", but that is just a manifest form of your own spirit - there is still a connection to your personality in everything a Conjurer manages to conjure, or how something is manipulated by a Manipulator and so on. And everything has a limit... everything.
Talking about training: How many other mangas/animes have managed to make training sequences interesting? I can't really think of any. They are usually just skipped over, or terminally boring. In "Hunter x Hunter" they are integrated in such a seamless way, and are accompanied by such interesting explanations, that they never become dull.
So... What makes "Hunter x Hunter" (2011) any better than "Hunter x Hunter" (1999) then? Well, it simply follows the Manga a lot more closely. Little-to-no real filler in each episode, and so far (as of November 2012) no filler-style episodes, apart from two recaps.
This is not to say that "Hunter x Hunter" (1999) is bad - not in any way, shape or form. It is a brilliant show, but the story is not as tight, and it tends to go off on tangents here and there - plus there is even some true filler episodes. If you can't wait to see what happens further down the line, then by all means check it out. Just know, that it actually ends quite some time before where the manga is at the moment - and it will, naturally, not be continued.
Anyways: sorry for the rant, but I just felt like the board deserved a truly massive post.
Quidquid Latinae dictum sit, altum viditur.