Seeing that there's no X-Men Origins: Sabretooth, I'll try to come up with an idea on how this change occurred.
So here are the things we need to consider. Wolverine aside from his adamantium didn't look much different from his appearance in Wolverine. Though he looks older in Origins than in X-Men, but we could reason out that he's healing factor might have rejuvenate his looks to make him look younger in the first X-Men movie. So, why is there much a lot more changes in Sabretooth: his height, his appearance, and his attitude.
My theory is that after the events of Origins, he now sees himself inferior to his "brother" so he seeks some ways to even the odds. Stryker has said that the adamantium bonding will kill him, so he looked for an alternate option in gaining a certain advantage against Wolverine.
Enter: Magneto. This one I think will fit well with the movie universe. In the first X-Men movie Magneto already has a machine that transforms humans into mutants. What if, the prototypes or other machines in a similar vein was the one that tranformed Sabretooth. There's your explanation why Sabretooth is working with Magneto on the beginning of the X-Men movie. The transformation would make him more feral, which will increase his mass and his strength.
How about the personality, why is there a big difference between the cocky Sabretooth in Origins and the Magneto lackey in X-Men. Here's my theory Magneto who has worked with Professor X on Cerebro, knows somethings as well about brain pattern manipulation. Seeing that Sabretooth would be an asset (much like how he saw Jean Grey "The Phoenix" in X-Men 3)he wanted him to be in his organization, though with Sabretooth being sort of a loose canon, he needed a way to have a hold in him. So with Magneto tricking Sabretooth into going into his procedure without the knowledge that he will alter his mind as well. Come the first X-Men movie, Wolverine and Sabretooth barely knows each other, though Sabretooth at the back of his mind still have a little connection with Wolverine when he got Logan's Dog Tag, and implying that he wants to be the one to kill off Wolverine. He barely articulates now and more often he growls.
-ACCESS out. Godspeed and MABUHAY