A big part of the freshmen English curriculum at my district is Greek Mythology. The main reason for this is that it's basically the backbone of all western thought (well, that and The Bible). There are so many references to the Greek myths throughout art and literature that a basic knowledge of the myths makes everything that comes later on (especially Shakespeare) much clearer.
Personally, I like to spend a lot of time on it. I manage to fill up the entire first quarter with Greek mythology. I give notes on all of the major gods and goddesses, and they read stories about Hercules, Pyramus & Thisbe, and Perseus (the last one I wrote my own version of it - perhaps I should post that to my blog some day). Considering that this unit covers so much time, I'm usually able to fit in at least two movies (if you don't count the assorted clips I show of Troy while they take their notes on Achilles and The Trojan War). I show O Brother Where Art Thou? after we finish The Odyssey, but about a month before that I show Jason and the Argonauts.
I know of a few other teachers who like to show Clash of the Titans, as that's a retelling of the Perseus myth. I like Clash, and I fondly remember seeing it with my father and older sister in the theater when I was just a little kid. Still, I only show a couple of scenes from that one, as I feel that Jason is the far superior film. Not only that, but they already got the Perseus story by reading it in class. This way, they get to learn yet another myth, but they get to take a break from all of the reading and note taking and learn it by watching the movie.
So, here are my reasons why Jason and the Argonauts is a better choice for a Ray Harryhausen Greek Myth/monster fest than Clash of the Titans.
#1: It's more true to the original myth. While they both take liberties with the story and swap out one monster for another, Jason is basically more like what the original story was all about. It's your basic quest archetype (think Indiana Jones and the Temple of Doom) where the hero has to retrieve a magic object that will restore a land to its former glory. That's the myth, and that's the movie. With Clash, Perseus is motivated by his desire to rescue the princess Andromeda. In the original myth, he just happens upon her while flying home. Basically, the movie overemphasizes the love story while detracting from what the story was really about.
#2: Hercules. I love the actor who they got to play Herc in Jason. There really aren't any performances that stand out in Clash. (To be fair, they're both filled with a lot of B-movie acting, but some of those actors play it off better than others.) Also, it's a good teachable moment when he abandons the quest for the Golden Fleece. (A major part of hero stories, and our the stories of our own lives, is that oftentimes we must get through our challenges without the aid of those who could help us best.)
#3: Jason is a more interesting hero. I've seen Clash dozens of times, but Perseus doesn't have anything about his personality that's particularly memorable. Jason, however, has a rebellious spirit. He openly questions the gods, and he (quite subversively, if you think about it) declares that the "gods of the Greeks are cruel! Some day men will learn to live without them!"
#4: You don't have to explain how once upon a time it was okay to show a woman's bare breasts and still have the movie be rated PG. That's right, Clash has boobs in it, and it even has some bare back female nudity. There's nothing sexual or inappropriate about it, but obviously there would be some who would beg to differ. In Jason, all the women are always completely clothed. (Of course, the bare breasts in Clash can be looked at as a plus on its side, but I'm writing about why it's not as good to show in the classroom.)
#5. Skeleton army. 'Nuff said.