DMA is newer and better. The exact technical differences? That's what Google is for.
DMA has lower CPU overhead and transfer rate is much faster. A few years ago one of my hard drives switched from DMA to PIO mode for some strange reason. When it was in PIO and I was trying to move a somewhat large file, say 50MB, Windows gave me an estimate of like 10 minutes to transfer the file from one hard drive to another. I also noticed my PC became somewhat sluggish.
It look a bit of snooping around to notice the mode switch. Needless to say, I switch the drive back to DMA mode, rebooted and all was fine again.
PIO is defintely way too slow. You would notice the difference if you are copying CD/DVD to you hard disk. If your CD/DVD Drive is set to PIO mode and you are copying a large amount of data from it. You may get an estimate of more than 40 mins for 700MB or something.
From experience I have found that PIO is good when the system is running unstable normally due to dodgy ram or data recovery sessions, although it is a slower mode I have found it more reliable during maintanence and recovery.