I love and own both of those movies!

Debating the merits of one theory of time travel versus the other seems like more of an academic exercise than a basis on which to judge a movie's worth, IMHO.
I also liked Donnie Darko and that indie film that came out a couple of years ago (forget the title).
As for who blew it, the latest Star Trek springs to mind. Can't they come up with a new concept besides time travel for these things? They've got the whole damn galaxy to play in, for pete's sake! And don't get me started on the idiotic villain who - instead of warning his people about their impending destruction - waits around for 25 years (doing what, I dunno; surfing porn on the Internet, I guess) until Spock is old enough to kill. What a steamin' heap o' buffalo loaf!
Haha, I'd never thought of that. For the record, I LOVE JJ Abram's "Star Trek", but yeah, if he's got time-travel, why the hell didn't he just prevent his world from getting blown-up? That's stupid.
The thing that bugs me about the time-travel in the latest "Star Trek" isn't whether or not it makes sense, but that it completely negates all other Trek movies before it. We're in a new universe -- none of the other ones have ever happened. That's bullshit. It pisses me off. They literally pressed restart on the entire franchise. Well, that's fine, in a way, I guess. But I like the old universe. I wish they would've found a way to blend old with new, instead of just completely sweeping out the old.
As far as the original question of this thread is concerned, to be frank, I don't think it matters too much, what type of time-travel rules they use, or whatever. As long as the story pieces together, that's all I care about. The entire concept of time-travel is quite silly, in my opinion, and I've never seen a time-travel movie that actually makes sense. Every single one of them has some kind of paradox that just smacks of nonsense. Half the time, I think the filmmakers did it on purpose.
For example, it doesn't take a rocket-scientist to figure out how nonsense the first two "Terminator" movies are. Okay, so in the first movie, we learn that in the future, John Connor sends back one of his most trusted fighters to protect his mom from attack from The Governator. And then, while he's protecting her, they procreate, the offspring which would of course be John Connor, himself. What?! That makes no sense!!! Clearly, Cameron created this paradox on purpose. He did it again in "T2".
In "T2", we learn that Skynet, and all of it's brilliant computer processing abilities were reverse-engineered from a small chip found in the arm that remained from the aftermath of the events in the first "Terminator" movie. Needless to say, this also does not make one iota of sense. It's fucking ridiculous, and I feel like it was intentionally written that way.
I'm actually very strongly leaning towards making my next feature a time-travel movie. As of yet, I haven't nailed down anything close to a solid story. All I've got bouncing around in my head is the concept of a time-travel movie combined with a mistaken-identity movie. A dude is suddenly thrust into a wild world, in which he has to unravel some kind of mystery, because he's mistaken for someone else. This is the classic mistaken-identity movie, no? Except, in my movie, he's not mistaken for someone else, but mistaken for a future version of himself. That's all I've got, so far. Any ideas?