Webroot looks like the culprit in my case too.
Having set WR to allow taskmgr.exe (https://www.webroot.com/En_US/SecureAnywhere/PC/Content/C5_Quarantine/CH5b_BlockingAllowingFiles.htm),the PC no longer slows to a crawl when Task Manager and Firefox are open.
To see whether the problem relates to the Webroot Filtering Extension in Firefox, I tried enabling it and disabling it. Didn't affect performance with TM open, so I assume that 'allowing' TM in Webroot is the step that matters.
I'll try Chrome later and report whether the WR fix holds good for it as well.
Unfortunately this didn't help when I tried it. Took about 3 minutes to regain control of my computer (2 Xeon Processors, 48g RAM, 1T SSD) when I tried opening Task Manager while Firefox was running after allowing Task Manager in Webroot.