If you are asking which is better - a serial port or a parallel port for PC-MCU comm. then a few issues are there as follows :

1. Parallel - Will consume 8 (data) + 2 ( Strobe & Busy )pins of the MCU for a simple implementation. Thats a lot if you ask me.
But the software that you need to implement this is next to nothing. And you dont have much timing issues as long as you can read the busy bit and sent the next character.
But first get the Centronics bus timings if you dont want to post another message here saying that nothing is happening. You have to make your own PC end software.

2. Serial - Just two wires + Gnd and if the MCU has built in UART ( which MCU doesnt have it by the way ? )the software is also simple. OK now the timing is an issue to resolve - but not a problem again - you just select the right crystal for the job after you do a simple calculation based on the Baud rate that you are looking for.
ANd as for softawre on PC end there are many terminal emulation programs - no need to write your own.

Raghu