I would use Gmail over Outlook any day. I trust Google because it is a major technology company with highly paid system engineers that get the job done right. When it comes to email security, you can be certain that you will be secure with Gmail. Gmail and Facebook both learn your login locations and devices so if they see someone log in from another country state or even City, they will deny access to the intruder and immediately notify you the next time you login. Outlook is great too but I don’t think it has those extra measures in place that Gmail has.
According to an article I came by in 2012, Microsoft said they are going to surpass Gmail in security.