Unless you're going out of your way to run your browser in a container or dedicated VM on Linux, there are substantial risks associated with browsing the web in terms of exposing all of your information in /home, which might include ssh and pgp private keys, basically everything your user can access.
But we have a number of solutions for running things in containers if you just use them. Early on firejail was popular, these days I just run nspawn containers for browser instances and bind mount in some stuff for a shared Downloads directory etc.
I can't speak to how that compares to OSX as I've never used it, but it is worth noting that the security story on Linux can range from bad to somewhat OK depending on your setup.
Edit:
In responses people seem to be completely ignoring that I already stated above in my original comment that I can't speak to how it compares to OSX. I don't know what OSX is doing for application sandboxing defaults.
I can however speak with some authority on the Linux situation. And today, if you're running firefox/chrome as your regular user as installed by apt/yum etc, without any additional sandboxing, and that user has access to secrets like ssh/gpg private keys, you're being unnecessarily reckless. And unfortunately that is basically the default way browsers are run today on most distributions
This is a major reason why the Flatpak/GNOME people have been working so hard on portals and namespaces are an integral component of the runtime. It's not just about application distribution. They're trying to close a major security hole in desktop linux as it's often used today. They want applications like the browser run in its own namespaces with just the minimum of host filesystem paths bind mounted in.
There's absolutely no reason for your browser process to have the ability to access all of your private keys, just because they happen to be under the home directory it happens to have access to, full stop.