With today's powders & bullets, the 300 H&H is better than ever, but I guess that is true for the '06 as well.
Both are competent & real performance is virtually indistinguishable, but whatever edge there might be in performance surely lies with the H&H, albeit, not a big edge.
And the "cool factor" surely lies with the H&H too. 
MM
Guessing that you figure "cool factor" differently than I do.
The 30-06 has oodles more history, and is associated with more of the coolest people than any brit round can lay claim to. Only the tweed coat/bwana crowd would ever attempt to debate the point.
I currently have an H&H in captivity, and hope to hunt with it this fall. It was the rifle package that drew my attention though, and not the chambering.
