In general, a dedicated hardware solution is going to be faster than a softare-based solution. To answer this specific question from my own experience:
When I got my "self-install" DSL package, it came with a 3-Com PCI modem that only supported Windows. I grabbed an old hard drive and did a fresh install of Windows 98 just to serve as an ICS host. Everything worked fine, but I was really disappointed with the speeds I was seeing from the DLS Speed Test sites (with and without Zone Alarm enabled).
So I bought an SMC 4-port router (found the $49 deal in the hot deals forum) and an external 3Com ADSL router. After switching over, the same DSL Speed Test sites were showing a 2x-4x speed increase. It's antecdotal, but the download speeds I've seen before and after the switch (ISO downloads to burn, newsgroup downloads) back it up.
I'm sure a Linux host running as a firewall and NAT (IP Masq) host would be faster than the same box running Win98, but it's not going to be nearly as fast as dedicated hardware (things like being able to forward packets before the enture packet has been received can be big advantages on the part of the hardware -- remember that the packets on a software-based host will need to be completely received, then passed up the protocol stack where a decision is made, then passed back down, etc. All of this leads to additional latency and reduced speeds).
Difference between Linux and Win98 as far as download speeds go? When X-windows is up and running on my 200 MHz Pentium Redhat 7.0 box (Gnome, Ximian, etc) Netscape can maintain 2 simultaneous 80-90k downloads; my 400 MHz P-II Win98 Laptop can maintain 2 simultaneous 49-55k downloads. Still antecdotal, but (I think) telling.
I say choose the hardware. It's worth the effort to learn something about routing, but a decent CCNA book ($50 -- call it part of the savings over building a Linux routing box) will teach you more than dinking around with an old PC.
All, of course, IMHO.