I have both on DVD. I like film history (I think Scorsese's two documentaries on American and Italian film are treasure troves to learn from), so I tracked down the original with Gregory Peck and Robert Mitchum, both of whom appear in the remake, of course, although in very different roles. Honestly, I like the original but I think it's one of those very rare cases where the remake actually improves on it. De Niro is every bit as intimidating as Mitchum. But more importantly, Scorsese goes into what's going on within the family in a much more interesting way. Just my opinion, obviously. Whereas Peck is the fine upstanding lawyer (he almost seems like Atticus Finch in To Kill A Mockingbird), Nolte plays quite a scumbag so it seems almost justified that Cady goes after him like a guided missile. Also, the sexual tension between Cady and Leigh, the wife, is completely absent from the first one; not to mention the sexual tension with the daughter, which is right on the limits of PC acceptability, and would have been completely impossible in the original. Then there is Elmer Bernstein's magnificent score. Loved all the biblical stuff, too, which Cady keeps quoting. That sermon he gives Sam Bowden, quoting from Silesius, when he's just beaten three men to a pulp and they're lying around him groaning is just brilliant cinema. The Old Testament is one of the bloodiest books in world literature, although people seldom realise it…
I've probably gone into this in much more detail than you wanted, but you did ask! And it's a film I'm very enthusiastic about. For me, it's up there with Taxi Driver, Mean Streets and Goodfellas.