It depends on what you're trying to accomplish. I'd go with option #2 if you're looking to transfer your rankings from the old site to the new. Once Google reindexes everything, you should have most of your ranks back.
If you're keeping the same content on the new site and the old, then option #1 isn't really an option, unless you canonicalize the old pages, which will have the same effect on ranks as the 301s.
So then it comes down to what's better for users? Do you think they would rather clickthrough the old site and its calls to action, or would they prefer to be automatically redirected to the new property?
I would think that you would want the new website to rank instead of the old, since having the old site continue to rank would just create an extra step for users.