I have had a little experience in the past running scripts that were created using Selenium IDE in a Windows 7 environment and the scripts ran just as well in Linux as they did in Windows 7. That could be more of a function of Selenium IDE than the FireFox browser but functionally it didnt appear to have much effect on my automation.
When working with browsers I have found very little variance on desktop OS's (Linux, Windows, Mac) other than maybe browser add-ons. It's been a while for me so take my opinion with a grain of salt.
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