Can't agree with Frank on this one. If you happen to own a high-end LD player, the Criterion LD is top-notch on both video and audio. The mono sound is crisp, the images filled with color and sharpness (except for some of the process shots). But that can be player-dependent. (If you don't have LD capability, no need to read further. Just get the DVD.) It is the only video version approved by Harryhausen.
Of even greater import to some is that the DVD has been altered to not reflect the filmmaker's intent. Harryhausen restored the intended look of the film for the Criterion LD and the DVD changed it so that it would "look better." (According to a published comment from a tech at the time.) One example is the Harpy capture sequence. This was shot day-for-night and is supposed to be a night scene, per Harryhausen. Often changed to daylight for TV showings, Harryhausen restored it back to the desired evening specs for the LD. The DVD changed it to sunset. The opening sequence of the movie was tinkered with on the DVD also.
And this, from the DVD/LD Newsletter: "Fleshtones on the DVD look somewhat orange, and fleshtones on the LD are much closer to true fleshtones. Many other hues (but not all) have a cleaner, truer look on the LD"