The problem is that the eye is not the most damaging part, it's the right side of the eye that's funneling water from the Gulf onto the land that's got the most damage potential. From that link it looks like New Orleans is in a much worse situation than if it were to receive a direct hit.
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There's that.
A near-westward hit could be more damaging than a direct strike, largely based on storm surge and possibly wind speeds.
What the maximal high-damage offset distance is I don't know, though 20--40km seems sufficiently close to be bad. I'd suspect a little nearer would be worse.
And I do wonder just how many more storms Nawlins and the Old River Structure have in them.