i think it's a little bit stilted in how they view each other, though in terms of regular character interactions they're still pretty brotherly.
it just always takes me out of it when they refer to each other as "my best pal/friend" and "bro" pretty much all the time (though there are sometimes in the early seasons where they call each other brother, like that part in Boom Boom Mountain which is nice) and it kills me immersion a tad.
it's less the way the relationship is portrayed, and more the way the show sets it up. I think it may have been a thing where the show didn't want audiences to think it's weird that this kid and a dog are acting like they're family members so they leaned on the best friend angle a bit more than later in the series.
this is a minor thing, but it does bug me because I love Finn and Jake's relationship and I want it to be framed in the way I feel it should be. do you know what I'm getting at?