I owned a '66 Corvette Convertible w/BB and sidepipes for about 25 years. I loved the car, but I sold it to buy the KMP. I couldn't justify two cars just sitting around most of the time. Though I have that anyway and more. But that's another story.
Go get the new Vette. If your '62 has a modern suspension, brakes and EFI, then that might give me a bit of pause, since I love the mix of old and new. But I'd likely still get the new Vette.
Having said all that, I can't stand the rear end of the C7.