I've used both Firefox and Thunderbird, but ended up 'moving back' to Seamonkey. My reasons for this move were the rather heavy load the combination of FF and TB puts on my - older - hardware as well as the fact that SM is more or less up to par with FF and TB while offering some 'convenience' functionality (eg. CTRL-2 opens mail from within browser, CTRL-1 opens browser from within mail). Another advantage SM has is that it supports the 'original' FF sync (which I use in combination with the Owncloud 'Mozilla Sync' app) without the need to jump through hoops. It also has a 'normal' preferences dialog, normal tabs, normal... everything. In other words, it did not succumb to the 'Chrome copy' trend which FF embarked upon.
Seamonkey happily provides me access to my mail (several accounts), dozens of open tabs in several browser windows and more in about 500MB of RSS. Firefox and Thunderbird together would use almost double that. While this might not matter on a recent system with 8+GB of memory, on this Thinkpad T42p with a maximum of 2GB it is a significant difference.
In general I'd advise against using the MailNews portion of SeaMonkey if you're also using the profile for web browsing. (MailNews is the guts of Thunderbird.)
MailNews results in a non-trivial amount of main-thread I/O that is going to badly jank your browser experience. The good news is that the worst of it will be when using the MailNews-related UI like switching folders for display, but it's still going to have an impact.
Although I'm close to ambidextrous, I have yet to manage the art of actively browsing the web while actively switching folders in the mail clients. Maybe if I had two keyboards attached to this machine it'd work, but I don't really feel the urge to try.
In other words, while theoretically a problem, in practice I don't see this as a viable reason to refrain from using both mail and browser in the same process space, ie. Seamonkey, not even on a relatively under-powered (1.8GHz Pentium M) machine.
Somehow, I didn't realize Seamonkey was still actively developed. I might give it a shot. I have an 8 GB machine, but even that's not enough when I'm running Android Studio and a Firefox with 40+ tabs.
Seamonkey happily provides me access to my mail (several accounts), dozens of open tabs in several browser windows and more in about 500MB of RSS. Firefox and Thunderbird together would use almost double that. While this might not matter on a recent system with 8+GB of memory, on this Thinkpad T42p with a maximum of 2GB it is a significant difference.