Out of the two they picked, I would go for Apollo 13 because I was a space geek when I was a kid so I watched it about as often as I watched the original Star Wars Trilogy (aka a lot).
With Forest Gump, there was always something...wrong about it. I know it was the story a mentally handicapped individual who went through life like many did in the '60s, except it felt so belittling to Forest as a character. Throughout the whole movie I felt like the director wanted us to sit and watch the troubled individual, who went through so much, and point our fingers at the screen. I can't explain it well, I only know that the movie never settled well with me.
Saving Private Ryan, while good, got shadowed for me by The Thin Red Line, which, imho, was so much better than the regular Hollywood WWII film they made with the former. Green Mile was another excellent film yet I think his best, for me, will be Philadelphia.
There, end of thread.