Wow. Not a response I'd expected.
The Live map allows one to zoom and scroll. I'll grant that you can do that with Map compare, but the caches displayed on the map compare are static, If you widen or shift your display area, you'll see no additional caches
The Livemap allows one to interactively filter. One could, for example, having examined an area, limit displayed caches to only Mysteries, and then, further limit to only those with the word 'challenge' in the name.
The only thing that, as far as I can see, that you can do with the MapCompare is save to a Virtual GPS, which is, of course, the very rub