Why does "The Affair" have two perspectives of the same story, and which one to believe?

It does not have two perspectives, but several and season five sometimes shows

three to four in one episode!

The first season is primarily "Noah" and "Alison", but the next season introduces the perspectives of "Helen" and "Cole" also.

Then in later seasons, there are more perspectives, such as

"Vic", "Whitney", "Janelle", "Seirria", and "Joanie".

And while episode 4.09 is said to be all "Alison" there are still two versions of the events, with the second showing a more aggressive version of events featuring a new character, which viewers can deduce is the "real" version, because of the results and how it pertains to the season finale and season five, despite that this other character is never given a title card for their part of that episode; or perhaps it's just the fantasy they have made up in their mind...

The reason the show goes back over the events is a stylistic choice to show that the characters have different memories to those events, whether that is because realistically we all see or "remember" ourselves differently than others do or because we tend to lie to ourselves and each other about whom we really are for various reasons.

Ultimately the executive producers want to make a psychologically-driven THEMATIC point about how humans are flawed and how we all can, to some degree, be "unreliable narrators". Sometimes however, a viewer can figure out whose perspective may be more [objectively] accurate based on collected data in future scenes or statements by various characters. The point is we all have a perspective or story and the subjective truth is not often black or white. This is what makes life and having relationships hard and this is the main thing a viewer should take away from The Affair.

This devise also generates suspense, as The Affair could at times be described as a psychological thriller and not just a relationship drama.

For those that are not familiar with Executive Producers and writers Hagai Levi & Sarah Treem, their previous work, In Treatment, also used a similar device where each episode would showcase a different character seeing their therapist, the main character Paul. And just like Noah Solloway, Paul blows up his marriage by having affair with one of his patients (Laura) that he thinks needs rescuing...

In some ways The Affair could be seen as an indirect extension to those ideas, since In Treatment was never able to finish it's story and because, it occasionally sneaks in a "therapy session" or therapy-related material.

In the first two seasons, Noah and Allison were interrogated by the police. The viewer basically sees the statements of Noah and Allison, and events happenening from a different point of view, or leaving things out on purpose. From season 3 on they just kept this style for the rest of the show.

Does the audience not get confused by this?

What I found interesting and somewhat confusing: Depending of the point of view, a character can be a nice person, or not a nice person at all. Then the show goes on and on and these things pile up, so that after a few seasons, you basically don't really know what a kind of person he/she really is. You never see the events from a neutral point of view.

This is merely the application of the famous "Roshomon" trope (see "tvtropes").