What determines the noise an aircraft's undercarriage makes at the moment it leaves the ground?
Without hearing it I would imagine that what you are hearing is the landing gear reaching full extension and hitting it's mechanical limit. Think of it like one of those bicycle air pumps, and the sound it would make if you pull that handle all he way up. It's the same basic mechanism, except upside down, and the landing gear should be full of hydrolic fluid to support the force of the aircraft landing on it. 

One aircraft has a mechanism that has a hard stop at the end of the stroke, and so you hear the extra forces being translated as that sound. The other aircraft has a softer end, so maybe there is a spring or rubber bumper pice or something that softens the end of the extension.