"will Google simply view the new as an extension of the old -i.e a part of it"
Google will see the new entity as a new website, even with the redirects. They will crawl all the new pages, and assign it rank based upon the quality score of the content, SEO, backlinks, etc etc.
The redirects can help with passing juice from one site to another, but as already stated they do not pass the full amount. The most helpful part of a redirect is for users, so when you change your website you can still be found.
I would see what the old domain has going for it. Look up the domain age, backlinks acquired through the years, social and citation links, current rankings, etc. Look for reasons to keep it.
In my experience, even if you do all your redirects perfectly and catch every single page, you will still see some form of ranking loss temporarily while Google indexes the new site. Seems like it throws them off for a while.
All that being said, if the new domain is catchy, easy for users to remember and has a keyword or two in the domain name, it may be worth it to change. I think it all depends how much work you want to do to get the new domain rocking.
