Advantages of parallel over serial connections
Parallel bus allows you to send more data than serial at the same frequency. That's it. This is why serial is more popular now than parallel. In the past it was difficult to have very high frequencies, so parallel was better.

For example:


SATA1 gets 150MB/s and requires at least 1.5GHz frequency.
IDE gets 133MB/s and requires only 66MHs.
PCI-e x1 gets 250MB/s for 2.5GHz
64bit PCI (server standard) gets 266MB/s for 66MHz


In the past it would have been very expensive (if even possible) to have SATA or PCI-e interface with the extreme frequency requirements.