That's a terrible question because so many dog-and-man comedies are really just chips off the classic buddy comedy block. Think about the classic Odd Couple--uptight guy vs. messy guy. Now, remember Turner & Hooch--uptight guy vs. messy dog. Free-spirits tend to come in and teach uptight people some things about life, and occasionally, vice versa. (Maybe Paul Rudd's Our Idiot Brother is really about a golden retriever--they're usually as affable as Rudd.)
In fact, the introduction of a dog--or a baby or a stoner--into an uptight person's life is a tried and true formula, and it doesn't totally seem to matter which it is for the general plot development, as long as it's one socially adjusted person and one socially maladjusted person. (Maybe this is why The Odd Couple endures: both of them are both adjusted and maladjusted and we take both their sides.)
(Similarly, many zombie apocalypses really set up some tension between the people left; so the zombie part could be replaced by many other types of apocalypse as far as plot development and character growth go. So, in these mismatch movies, it doesn't matter what the mismatch is.)
So, what about Wilfred, the tv show where Ryan (Elijah Wood) is a social drop-out--he doesn't want to be a lawyer and the first episode involves a suicide attempt, which is really taking "maladjusted" almost too far--and he meets the dog Wilfred, who he sees as a man in a dog costume (Jason Gann)? Who's the socially-adjusted one?
The dog in human society is definitionally maladjusted, as evidenced by the times when Ryan follows Wilfred's lead (shitting in a neighbor's boot, having sex with a stuffed animal). In other words, we put up with a lot of dog's behavior because they're dogs and don't know any better. But in Wilfred, from our POV, seeing a man act like a dog reminds us how this is inappropriate behavior.
But Ryan, as I already said, is no Felix--he tries to commit suicide, he smokes a lot of pot, he talks to a dog. But I think there's still a tension there in that Ryan has the possibility of being a socially adjusted human, whereas Wilfred, not so much. (Oh, this just makes me want to read Bulgakov's Heart of a Dog, where a Soviet scientist turns a dog into a man.)
Or maybe recent buddy comedies and other sitcoms (following Seinfeld's lead?) have changed their dynamics; as with It's Always Sunny in Philadelphia, maybe there's no desire to have a nice, normal person to play off against the others--you just need everyone to be cracked in a particular way.