What business advantages does Outlook give over Gmail?

As an e-mail client, Outlook is unexceptional. The driving difference is whether you want the overhead & control of hosting Exchange, or are content letting Google take care of that.

There are many more features Outlook support especially if your firm runs an Exchange Server. Only the Outlook client can take full advantage of all the Sharing of Calendar & Contact features.

...as you can basically use gmail from within Outlook, but you can't run (why would you) outlook from within Gmail. Two different approaches to a same dilemma: how to manage your email. I prefer Outlook to work. I'm just used to how it works and the many options for writing, reading, completing emails. Throw some nice Office add-ons and you're done. The one thing I hate is that after more than 13 years, outlook is still using that crappy "one file for everything" system, while mails are just mails in Gmail. Know what I mean? One can crash and destroy your work.. The other one is Gmail.

I agree that the integration with Office is nice. You can use Outlook as your e-mail client and not be using Exchange Server. Probably the biggest advantage is that Outlook is the defacto standard in the business world.

There are several. One main one is that your email is stored (with Exchange) on your own server's rather than Google's. Also, there is built-in MS Office integration.