The best protagonist is one that is 'real'. I don't mean they can't do things like magic, or can't spawn random tentacles on a whim, or pop brains from afar. Rather, a real protagonist is one whose motivations are clear, and if I were to know what they're motivation for doing something is, then their story would make sense -- even if it was batshot idiotic.
I'll use an anime as an example (forgive me for my niches). In GunXSword, Van the protagonist accompanies a girl, Wendy, on her journey to find her brother who has gone missing. Van could care less, as his motivation is to find the man who killed his wife. Thus, knowing his motivation, everything that he does relating to this plot should be caused because he is looking to find the man who killed his wife. For example, The only reason Van allows Wendy to accompany him is because they are going the same way. The only reason Van meets the people he does is because he is looking for this man. If he wasn't, none of this would be happening, and that makes him real.
A bad protagonist would be someone who 'saves the world just because'. Someone who goes on an incredible journey just because someone told them to, while their motivation would be something akin to 'chilling at home and eating pizza'. These protagonists don't feel real and there are so many of them, but the good ones are the ones we remember, like Lara Croft, Solid Snake, even Link has motivations -- his only wants to protect Zelda. Before that, he's basically nobody.
So, to sum up, the real protagonists are the best protagonists, and the best protagonists are the coolest. Hell, even Ocelot is cool and he's an antagonist, but his goals are clear and he feels real and someone, somewhere in the world, should relate to him.