The GameCube uses a Panasonic DVD-RAM Drive, while the DVD-ROM of the X-Box and Playstation 2 are 4x DVD 2-Layer.
DVD-RAM is just simply better than DVD-ROM, there are no two ways around it. The main reason for this is the CAV (Constant Asyncronous Velocity), it allows the disc to be constantly moving and read from several points at any given moment.
It allows the drive to constantly be streaming data, much like a Hard-Disk can.
Also you factor in the speeds at which these drives can read at.
DVD-ROM reads at 4.2MByte Per Second, DVD-RAM read at 23MByte Per Second.
It doesn't sound like much but given that even a SATA 150 Hard Disk is only capable of 18.8MByte Per Second, it's not hard to see why the DVD-RAM is such a good choice as the drive.
Hard Disks Tend to overcome thier slower speed with Cache, to a degree so do DVD-ROM; but as I said above the DVD-RAM doesn't need Cache because it just streams directly to memory.
It's a shame that Panasonic weren't the ones who won the DVD Format battle; because DVD-RAM is just better.
Designed to read despite scratches, Capable of Seemless I/O, Capable of Multi-Track I/O, Upto 4-Layers Providing almost 17GB of Space.
BluRay has achieve what DVD-RAM did, simply by enhancing the beam; so you can image what Panasonic have done for DVD-RAM+
Look forward to thier BluRay edition of DVD-RAM over the next year, should prove to be very interesting.