I'm planning to build a home server, just to setup a file sharing (hooked up to an external HDD) and a torrent daemon. Between a Raspberry Pi and an older Tp-Link WR1043ND Router, which would have better performance? Th R-pi has a better CPU by far, but the router has probably a better network controller and was designed specifically for such an application
The Rpi has a better CPU and far more RAM, but the WR1043ND has got gigabit Ethernet.
Depending on which file sharing protocol you plan to use (samba, nfs, ...) one could be better than the other.
The router is a good option to try, since it's probably already an always on device anyway.
About the performance, installing and trying a file server on both will probably take you 10-20 minutes.