I think Oceans 11 is better than the original.
I also think that Heat is better than LA Takedown. Technically two different titles, but Heat was just a longer, larger budgeted film than LA Takedown and both were directed by Michael Mann.
However, even though the remake of Cape Fear was excellent, I do feel the original was better as Robert Mitchum was more menacing than Robert De Niro (and I love RDN movies) and the violence was left more to the imagination.
Overall, I do think that good original movies tend to be better than good remakes, but there are the occasional exception to the rule. The 1976 version of King Kong was pants compared to the 1933 version. It will be interesting to see what Peter Jackson does with his version this year.....