In the X-Men Origins, assuming Adamantium replaced his skeleton, he had ugly bones coming out of his hands, so Adamantium should have taken their shape, not nicely shaped blades. So was there a different explanation for Wolverine's claws or is it just so?
I've not seen Origins, but this has been inconsistently displayed through the comics.
I believe that, in the most recent canon I've read, Wolverine's claws are bone, laced with Adamantium like the rest of his skeleton. This makes sense (in the comic book usage of the term, at least) because if the claws weren't part of his original skeleton he wouldn't have had the musculature in place to extend or retract them.
As for the appearance in Origins, I can't answer why they would appear rough. I would expect that any claws would be similar to a cat's - smooth on the sides. They wouldn't be curved, of course, as they have to be stored in the forearm while retracted. It's likely that the Adamantium bonding would fill and smooth out any irregularities as it plated the bones, which could account for the visual difference you point out.
The Adamantium didn't replace his bones, they just covered them. So, technically, they could have taken any shape the scientists wanted.
As for the shape of the claws, it is a well known fact in the X-Men universe that most mutant abilities activate only during a heightened emotional state during puberty (with some exceptions of mutations at birth). So, I propose that Wolverine's claws didn't appear until during puberty, which could explain why his body hadn't smoothed out the claws yet.