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.