if you're using the Linux box just as a router, it would do the same thing, but generally allow for finer tuning and the installation of other software such as IDSes and whatnot on it. It could NAT (your internal IP addressing scheme, DHCP or otherwise), block all unecessary ports, etc.
The thing that really generally makes a "hardware router" more secure for home users is that it is a separate dedicated piece of hardware that's simple (which is always better in security terms) and expendable. If it gets compromised, there are no files to steal or anything, though the intruder likely has access to the internal network at that point, if they didn't just cause a DOS. Even if that were the case at my house, for instance, my internal machines are then protected by iptables themselves. Though I guess the intruder could print to my printer and such or exploit weaknesses in it to attempt to gain access otherwise.
It's never a good idea to have your border routing/firewalling done by a box that you use all the time. It should be as simple as possible with as few things exposed as possible, whether it's a stripped-down, cheap Dlink, a dedicated Linux machine, or a Cisco PIX.
Does that answer your question?
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