In my opinion you need both: A cd-rw to copy the cd based PS2 games and a DVD-RW (such as the Pioneer A04) to copy dvd based PS2 games.
I would use Clone CD to copy the PS2 cd based games.(If your burner is 100% compatible) Check to see if it is
HERE!
Then use Prassi Primo DVD to copy DVD based PS2 games....
You can get Clone CD & Primo DVD
HERE!
And you can get tutorials for both
HERE!