Are there any advantages to installing a parallel port in a C1541-family drive and using a parallel cable to a PC to image disks, other than increased speed (i.e. since the standard IEC protocol is serial, one bit at a time)? I got the impression years ago that some nibblers (i.e. very low-level copiers, for things like copy-protected software) only work with parallel, but I can't reason out why.
Nibblers that are utilizing opencbm on a PC need a faster-than-stock connection to read the GCR encoding in real time. There are a couple of solutions, the most common of which requires a ZoomFloppy. To nibble from a 1541 requires a parallel port. 1571 drives are much faster due to better hardware, allowing ZoonFloppy to nibble over serial.
For PC connectivity you win absolutely nothing. Various devices that allow connecting a 1541 (and others) to PC will still talk IEC to the drive, regardless whether they use USB, serial or parallel to PC.
There are two devices that are praised for their data transfer abilities - ZoomFloppy and KryoFlux - the former uses IEC as well but has optional connectors for the drive (and you could use it with a 1541), the latter talks directly to the drive.
There exists a parallel interface for 1541 that connects to CIA chip in a C64 - that allows for much faster transfer because it bypasses the IEC bus completely. But there are no devices on the market that would use such connection to a PC.
A parallel cable helps to copy special formatted disks with an original drive connected to a C64 or even a PC. The problem is the limited RAM (2 KB) on a 1541 that prevents to store a full track keeping all details of the format. With a parallel cabling it's possible to transfer on the fly of a full track. An example for such a picky format is GEOS with its original disk-set. The gaps between the well-ordered sectors are carrying special information to prove the disks are genuine (sorry, I have just a german reference GEOS-Kopierschutz).