It is less costly to design ever faster serial lines than to create and build the necessary circuitry to keep faster parallel channels properly aligned. This is why Parallel ATA and Parallel SCSI have migrated to Serial ATA (SATA) and Serial SCSI (SAS).

one bit at a time vs. a group of several bits at a time.

Depends, is the device serial or parallel?

parallel

Some key differences between a Serial and Parallel Adder are that a Serial Adder is slower, a Parallel adder is a combinational circuit and the time required for addition depends on the number of bits in a Serial, but not a Parallel. A Serial Adder is a sequential circuit while a Parallel is a combinational circuit.