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.