I put forward a vote for One Piece. While debatably Naruto is more widely known and loved, (mostly due to that godforsaken 4kids dub of One Piece), and admittedly, Naruto typically has slick combat, decent characters, and a pretty good storyline, Naruto is the only character to have really gained growth over the course of the series. The other characters are obviously side characters, and don't have anywhere near the same level of development as Naruto. This is fine, since Naruto is the protagonist, but compared to One Piece, all the members of the Straw Hats have equal character development, they all have their own back stories and reasons for joining the Straw Hats, each of which have an entire arc to develop these. Compare, say, Zoro to... Sakura.
Prior to joining Luffy's crew, Zoro was a brat who wanted to become a great swordsman. Joining a kendo school, he became rivals with a female swordswoman named Kuina. After 2001 consecutive losses, Kuina revealed that she believed one day Zoro would beat her because he was a man, and thus would get stronger as he grew older, while she wouldn't. After that, they both swore to one day become the world's greatest swordsman. Shortly thereafter, Kuina died, and each time Zoro is on the edge of defeat, he draws upon her memory to drag himself up from the dirt.
Conversely... Sakura. She... used to like Sasuke? Had a crush on him? Oh, and used to be bullied about her forehead.
Each of Luffy's crew has something they are on his crew to do, Zoro wants to be the world's greatest swordsman, Sanji wants to find the All Blue, Nami wants to chart the entire world, etc. While some Naruto characters have revealed a desire called their 'Ninja Way', such as Rock Lee wanting to become a great shinobi despite his inability to use jutsu, none of them have a real desire to do something to the degree that the Straw Hats do. And because we know what drives the Straw Hats, WHY they're doing what they're doing, we are more emotionally connected to them, and have even more reason to root for them.
Oh, right. Bleach is in this poll too.
Bleach... Bleach... Bleach... Where do I get started on Bleach? Okay... hmm... Okay, I've got it. Bleach has really great animation for the anime, easily rivaling the usually ridiculously high quality of anime movies. The battles are pretty incredible, and the constant back and forth will have you gripping your seat with no small amount of tension. Which is usually dispersed rather quickly at the end with Ichigo suddenly winning out of nowhere when it had appeared he'd been soundly defeated. While the Straw Hats are usually beaten within an inch of their lives in their battles, and have to use every ounce of spit and blood in them to pull out a win, a battle in Bleach usually works like this:
The two characters begin fighting each other. The enemy reveals everything about their own abilities. The good guy (or girl) analyzes for weaknesses, believes they've found one, and hits it. Enemy powers up to second level, and begins soundly beating the good guy. Good guy gets to the edge of defeat, and reveals it's either been an elaborate set up, or suddenly develops a new power or gets a reason to stop holding back aside from, y'know, saving their own lives. Good guy immediately wins.
I'm not saying their aren't exceptions, but that's the general formula. Conversely, fights in One Piece can really go either way, the Straw Hats have had their fair share of losses. The only real loss I can think up for Ichigo off the top of my head was versus Byakuya the first time. Oh, and Aizen. On the other hand for the Straw Hats, we have both of Luffy's encounters with Smoker, Luffy's first encounter with Crocodile, Zoro's first encounter with Mihawk, the entire Straw Hats first encounter with Oars, Zoro's first encounter with Kuma, Luffy's first encounter with Magellan, the entire Straw Hat crews encounter with Kuma and Kizaru, to name a few.
Not to mention the different worlds. Naruto exists in a rather interesting world of shinobi, where the governing force and military are all ninja, and with the exception of medical facilities and occasional communication equipment, appearing to exist in the feudal era. Bleach exists in the modern day world, while occasionally visiting other realms such as the infinite desert known as Hueco Mundo, or the massive afterlife city known as Soul Society. And then we have One Piece, which exists in a world of pirates and Marines, which is filled with incredible creatures and incredibly odd people. Once again using the Straw Hat crew as comparison, you have a green haired swordsman, a cycloptic chef, a money obsessed weather manipulating cat burglar, a long nosed liar, a doctor deer, a multilimbed archaeologist, a blue haired speedo wearing cyborg shipwright, and an afro skeleton musician. Oh, and Luffy, the man made of rubber.
Their competition is Naruto, an orange wearing, 'believe it', spouting, ninja.
And Ichigo, an orange haired, half-death god.
Please don't misconstrue my arguments against Naruto and Bleach as me saying that they're bad or anything, if you have the time, check them out as well. Bleach had a time-skip recently, so it's pretty easy to get into it if you want, and like I said, the animation is slick, and there are some occasional funny moments. Naruto as well. Just in my opinion, if you have to choose one of the three, pick One Piece. They also had a time-skip recently, so still easy to get into, and I think you'll find it a lot funnier, a lot more often than the other two.