Bradbury`s 1952 story "The Sound of Thunder" about a tourist who goes back to the dinosaur age and steps on a butterfly, making the present much worse when he gets home, is the source of the term "butterfly effect" about how small changes can have big results.
In contrast, Heinlein`s 1941 time travel story "By His Bootstraps" is a good introduction to the paradoxes of predestination in which the time travel all unfolds as fated despite the best character`s best efforts to change the past.
Then I glanced at the ring on my finger.
The Snake That Eats Its Own Tail, Forever and Ever. I know where I came from - but where did all you zombies come from?
I felt a headache coming on, but a headache powder is one thing I do not take. I did once - and you all went away.
So I crawled into bed and whistled out the light.
You aren`t really there at all. There isn`t anybody but me - Jane - here alone in the dark.
I miss you dreadfully!
Back to the Future sides with Bradbury, and that`s a pretty good movie.
On the other hand, you could argue that Sophocles` Oedipus Rex is a proto-time travel story that takes Heinlein`s side. How does the Oracle know that Oedipus will kill his father and marry his mother? Maybe she has a time machine!
And that plot works pretty well, too.
I was thinking that maybe Bradbury`s changeable history makes for better comedy and Heinlein`s deterministic history makes for better tragedy, but perhaps the opposite is true. The gyrations that a Heinleinian time travel plot has to go through to make everything wind up being the same are often exhilaratingly comic, while Bradburyesque plots like the new Looper, which takes a strong stand at the end in favor of [Spoiler Alert!] mother love, often tend toward the sentimental.