It depends. Because you will be the only entity to store your entire mailbox, I guess you could consider it more secure in that it is not sitting in a data-center somewhere being mined for advertising data or for science. Still, email is an inherently insecure medium. Unless you specifically use end-to-end encryption, any mail that you send is 'in the clear' once it leaves your network. That is, anyone who has access to that network and basic free tools can read your mail in its entirety. Nobody uses real encryption because there isn't a standard - both the sender and receiver have to agree to use the same standard ahead of time, and it just hasn't been done.
I would also argue that unless you really know what you are doing, your email at home may be more at risk to hackers than leaving it to a professional service. The best thing you can do if you use a service like gmail is to make sure you access your account via https rather than http. Fortunately gmail finally made this the standard recently. If you do this, your connection to gmail will be secure, although once gmail's mail servers relay your message it will be in the clear - but for most people the most dangerous spot in their email's journey is when they log in to retrieve it themselves, particularly on an open hotspot. Https secures that leg.