I have multiple email accounts from different providers: gmail, yahoo, etc. as well as more secure, privacy-minded services that use heavier encryption. Right now I access them all through a web browser, namely Chrome or Firefox, primarily in Windows 8.1 or Mac OSX Yosemite, although I also use Debian at times. Knowing that web browsers are historically pretty vulnerable pieces of software, I've often wondered if I should be using a Mail Client like Thunderbird or something similar instead of accessing my email through a browser.
My question is, how do mail client's compare to using a web browser for email, in terms of security and general vulnerability? Obviously if somebody is able to get remote access to my system, all bases = theirs no matter how I'm using email. But is one or the other more vulnerable to threats like interception/man-in-the-middle attacks? I'm especially interested in differences of how the different solutions handle encryption, TLS, and how they work with the security I have in place on my different devices.
I use some basic security measures like using a VPN and a firewall/monitoring software so I can manage and watch incoming/outgoing connections. The obvious stuff like anti-virus/malware/spyware and some script management plugins for the browsers, keeping things updated and so forth is also taken care of.
As somebody who has never used a mail client, the final part of my question is can you recommend a security-aimed mail client, or even better, give me some details to look for when I'm shopping around for one?