If your PPI ( programmble peripheral interface) refers to the I/O ICs or cards that were tradtionally based on 8255 is a general purpose input/output IC, then there is no much poin in asking "PPI or relay" question.
In very many application a relay is needed between the computer interface (this could be parallel port, industrial I/O card with 8255 PPI ICs in it etc..) and the load being controlled. The computer interfaces generally are deisgned for very low power loads, operate at low voltages, and get damaged easily. The relay between the computer and load allows you to control higher voltages (up to mains voltage or even higher), higher current (many amperes with normal relays, tens of amperes with very heavy ones) and they provideo isolation form load to computer (needed for safety reasons when dealign with mains voltage).
Almost the same type of relay interface (maybe at some cases exactly same circuit can be used) is generally used between the computer and the load being controlled no matter if you use a dedicated PC I/O card or PC parallel port for the controlling.
Here is one description of how to control mains voltage loads using industrial I/O card that has PPI chips in it. The description is from Planet Christmas web site page at
http://www.planetchristmas.com/Digital.htm and
http://www.planetchristmas.com/BlueBox.htm
"PlanetChristmas uses boards from a company called CyberResearch (
www.cyberresearch.com). They have a series of "Digital I/O Boards" which plug into a PC ISA slot so you can control the outside world. In 2002, a 24 I/O port board (part number CYDIO24) costs $47... a 192 port board (part number CYDIO192) costs $199. They also have 48 port and 96 port versions. "
"Each of these I/O lines is connected to a solid state relay (3-5VDC input, 120VAC output... they typically cost $5-$18 each depending on the current load (I use a 7 amp rated version from Magnecraft.))"
"Each of the computer I/O lines (called a circuit) is connected to the appropriate strings in the yard. Most circuits are in groups of four or eight so chasing effects can be used. Here are some closeup pictures of a solid state relay box. To see a simple electrical schematic, click here."
http://www.planetchristmas.com/BlueBox.htm
Picture source:
http://www.planetchristmas.com/BlueBox.htm