I'll take this thread in another direction, that may (or may not) shed some light on the topic. Bearing in mind the concept of a Polytheistic Mythos is, like most religions, a backdrop for our own morality plays (see: Greece/Rome, Egypt) we can look through a couple of different lenses.
For one, the idea of 'competing Gods' can be a campaign structure in itself. Gods may be attempting to knock off other deities to consume/assume their portfolios or because they flat out don't get along, for whatever reason. See: FR: God Wars, also, Egypt: Set vs. Osiris, Greece: Hades vs. Zeus, Norse: Loki vs. Thor. In a campaign structure, these two sets of followers could be 'acting out' the battle being waged in the heavens, hence they are in direct competition, from sabotage, to who does more for the community, to all out war, despite having differet portfolios. In the case of Loki vs. Thor, the two have almost nothing in common; Loki is portrayed as either CN or CE, and Thor is classically CG (God of Thunder and all that, likes the ladies, but is still on the side of 'good.' Bit of a partier to be considered LG). So now we have (and can have, in multiple ways) situations where they compete despite the idea of portfolio.
Let's pull it back a bit, and the Gods themselves are, as was posted earlier, merely the Incarna of other people's beliefs. Then you'll have a group of people constantly attempting to convert/alter the faiths of others to your new faith (See: OOTS, Banjo the Clown). "Cthulu for President! Why choose a lesser evil?" In this scenario, the Gods are real, but real because they were made 'real' by their followers. This gets into ideas like collective subconcious that I won't go into for this thread, suffice to say, the more people pray, for whatever reason, the more powerful the God becomes, always questing to no longer need followers (i.e., to become a Real Boy, instead of a powerful idea). That would make one helluva campaign, now that I think about. I should write that one down. Moving on.
And, of course, the idea that the Gods aren't directly involved in the way we think of them. Competition is nothing more than folk tales and stories; there's no hard evidence that they exist. Yes, Clerics cast spells, and THEY claim there are Gods, but what does that mean to the local Wizards Union? Not much. Sure, they have a Priest of Azuth, but hey; who doesn't? Now it truly doesn't matter who your patron deity is, because the belief that they grant spells is what's getting your Clerics their magic; not the Deity themselves.
Good morning!