As far as I know, there is only one download of Firefox Browser for Android in the Play store. However, I imagine that it checks your screen size/resolution and may offer additional features for those with larger screens. Why not give it a try? There also is a "beta" test version available if you want to see a version with forthcoming features.

I missed the part about synchronizing emails. Neither Firefox desktop nor Firefox mobile is an email client; instead, you would generally use them to visit your email service provider's webmail site. Your email service provider will allow access from either browser to the same email folders; no other synchronization should be needed.

I assume you can access your mail using the stock Android browser??