The choice of browser is something of a personal one, though Linux is well-served in this respect. We're kinda spoilt for choice.
The drawback with browsers, for most folks, is that for each distro you have to install the browser from scratch again. In years gone by this meant maintaining bookmarks and stuff like that, since you would end up with stuff in one browser install that wasn't in the others. Then "sync" arrived, which made keeping everything identical much, much easier!
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I'm not keen on "sync". Google's syncing is too nosey, and Mozilla's seems a bit haphazard for my liking. So instead, for Puppy we developed our own version of the Windoze 'portable' apps (which also keeps all config stuff within the app directory, too)......initially, browsers and stuff like Thunderbird, then soon followed by portable versions of no end of other applications.
In this sense, 'portable' means you can run each item from outside the OS itself.......and because of this, it's entirely possible to 'share' an item between several OSes. This also cuts down on app duplication and overall waste of drive space. This way, I've achieved my own "syncing", and the beauty of this approach is that the data all remains 'local', and under the user's control.
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The system works very well for us here in Puppy Linux, due to Puppy's somewhat unique and slightly 'oddball' approach to things.....running in a virtual filesystem in RAM, loaded-in from read-only system files in squash format, and possessing the ability to run several Puppies from individual sub-directories within a given partition.
I somehow doubt it would be that successful in mainstream distros, however.
Mike.