There was a bug in the serial hardware on the C64 that required them to seriously drop the transfer speed. The slowness was a result of having to deal with that bug.
SATA on the other hand uses 2 differential pairs (One Send, One Receive, simultaneously) which you can drive a lot faster with more noise immunity than a single-directional bundle of parallel wires with only a high or low signal that is extremely susceptible to electrical noise.
To put it in an ELI5 fashion..
With a PATA drive you have 16 pairs of people having a single slow back-and-forward conversation in a crowded room of other people talking.
With a SATA drive you have 2 pairs of people having entirely separate conversations where one person is listening while the other talks extremely quickly in an empty room that is almost completely silent.