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I have two POV (3rd person limited) characters and they start the story as complete strangers and far apart. They don't meet for some time and they have very different experiences.

Now I want them to meet and live through some intense, important event. How can I choose whose POV to take during the event? They would have very different views of the same event and I want them both to convey their version to the reader. But I don't want to tell the same event again.
What should I base my decision on?

You have different options:

1. 
   

   Often, when a novel is told from two viewpoints, the distribution of viewpoints is systematic. For example, all even chapters are told from one viewpiont, all odd chapters from the other. Or one part of the book is from one viewpoint, the next part from the other.

   
   
   

   If that is how you divide viewpoints, simply use the viewpoint whose turn it would be.

   
   


2. 
   

   Chose the viewpoint of the character who

   
   
   
   
   
   • undergoes a change in the chapter
   
   
   • is the agent of change
   
   
   • is the victim
   
   
   • etc.
   
   
   
   

   Depending on what your story is about, what its theme is, how it ends, and so on, you should have a gut level feeling of whose viewpoint

   
   
   
   
   
   • drives the plot forward
   
   
   • doesn't give away the plot-driving riddle
   
   
   • provides more information or entertainment for the reader
   
   
   • etc.
   
   
   
   


3. 
   

   You can head-hop, that is, mix viewpoints from paragraph to paragraph, or even within the same sentence.

   
   
   

   Stephen King is famous for this, and even Hemingway did it.

   
   

In the end it's up to you, but I think you haven't explored all of your options so far. You could also alternate between the characters views to show how different the situation feels for both of them. This makes it intense for the reader because they can read both points of view without anything feeling like they have to re-read stuff. You just have to be careful not to do this for a prolonged time or the reader might get a little exhausted from this practive. But for a relatively short and intense scene this can be perfect. And if you already switch between different characters, for example every chapter or so, your readers will already be accustomed to their individual "voices" and the fact that you are switching between characters. Just be sure to make it obvious when you switch. For example by regularly mentioning names, using specific phrases and using proper formatting that conveys a change in your story-telling.

To find the answer to your question simply list all options you have found by thinking about it and by asking other people and write what you think is good about the approach and what is bad about the approach in regards to your specific scenario. Think about your target audience, the length of the scene, the intensitiy / speed of the scene, the feelings you want to convey and how different this is from your usual approach.

The POV should probably go to the person with the most "stakes" in the scene, the person who experiences a bigger "life impact" or "state change" to their character arc. That is the character who will most likely be the focus of reader sympathy.

This is not necessarily the most vulnerable or most emotional, and it may not even be the one who is doing the most action (or having the most action done to them), rather this is the character who – whether by participating or observing – experience a turn in their story arc development (not necessarily the one with the most plot or action).

For example: In a final contest between rival Characters A and B. Character A is the handsomer wittier athlete, charismatic and the favorite to win. The POV might go to Character B because she has a realization about the purpose of the contest, and it changes how she views the system that rewards winners and punishes losers. Or it might go to Character B when she realizes she doesn't care about winning, or that she would rather loose fairly than cheat to win. The "plot" seems to point at A being the more important character, but B is the one who is having a turning point in their character arc.

In many cases, the POV goes to a less important character because the more visible character can't tip their hand to the reader, think Watson and Holmes. Holmes is cleverer and smarter, but Watson experiences more "stakes" because he does not know the outcome of the mystery.

Coming of age stories probably follow the least experienced and least important person in a household, but who has the farthest to grow, or who makes a life-altering realization.

Write the chapter describing the event twice, once from each point of view. You can even write it from a non-POV character's POV as an additional exercise. In the end, this is the quickest route to the best story (and you learn the most about your characters this way) although you may not want to hear to write it twice.

After you have the various versions down, pick the one that is strongest and most impactful. Many 2-POV novels have their main characters meet up along the way (usually early) and so this is a problem that is commonly encountered.

In terms of having the non-POV viewpoint be radically different (but known and clear to the reader), you do this by establishing viewpoint prior to the event to such an extent that the reader knows exactly what the non-POV character is thinking--even though the scene is not in that character's POV.

Imagine a 2-POV story with DJTrump and a sweet, young beauty contestant who has never met him and knows nothing about him. Imagine the scene when they meet for the first time in the back stage area of the pageant, with all the other contestants. Imagine it from the girl's point of view--even if she is thinking what a kind and generous man Trump is, for taking the time to come and visit all the girls back stage and ask after them, and offer to buy them things, and he says he thinks they're all fantastic, 'what a nice man,' she keeps thinking, WE know her perspective is off because his POV has been so firmly established prior.

One thing that I've seen that was used pretty effectively was to repeat the scene from each perspective; with, possibly, different start and end points.

It takes a bit to make sure the readers know that they are reading a repeat but I've seen it make for some good reading.

I essentially agree with all prior answers, but I'd like to offer a suggestion that I think is missing:

If you decide to choose only one character as the OV character for this scene, I would submit that you choose the POV of the character that knows less about the situation than their counterpart.

This can play out in two different ways, both beneficial to your story.

The first is that the reader doesn't yet know everything that you'd like them to know about the situation. By putting them in the shoes of the less-informed character, the character can ask questions/have reactions/gain knowledge in sync with the reader, inclining the reader to "connect with" the less-informed character in a way that would be impossible for the more-informed character.

The second is when the reader does know everything about the situation. In this case, the reader is held in mild suspense, trying to figure out when the less-informed character will find the truth, and likely "rooting" for said character.

Obviously, this won't work in all situations, and might not in yours, but it's my two cents as a general suggestion.