But only two of her children survived/would survive.

[WilliamTaft]

Source: VOA Learning English - America's Presidents - John Kennedy: Young

She (JFK's wife) became pregnant five times. But only two of her children would survive: a daughter named Caroline, and a son, John F. Kennedy, Junior.

What's the difference if I say "survived" in this context?

 

[Tarheel]

In my humble opinion "survived" would be more natural in that sentence.

 

[teechar]

"survived" = speaking now about an event in the past.
"would survive" = going back in time to a point in the past (X) and speaking about an event/situation that happened after that point (X).

 

[Tarheel]

Source: VOA Learning English - America's Presidents - John Kennedy: Young

She (JFK's wife) became pregnant five times. But only two of her children would survive: a daughter named Caroline, and a son, John F. Kennedy, Junior.

What's the difference if I say "survived" in this context?

You are describing the same thing in either case, but as it is pointed out in post #3 it's a matter of perspective. With "would survive" you're putting yourself in that time looking towards the future.