I disassembled some 250w metal halide ballasts and was amazed at the size of the transformers. I would estimate that they have 3-4x the copper and iron as the microwave oven transformers rated at 1500 watts. I've read somewhere something about MOT's and saturation, which I'm not really sure what this means and if it was fully saturated or not...

The design of the transformer was also different between the two. The Ballast was arranged in a linear fashion with the laminated steel plates running through the middle and the wires wrapped maybe 2/3 (primary) on one side and the secondary covering the other 1/3 of the core. I can't remember is there was any exterior steel laminates but I kind of remember that there was.

Even if the ballast transformer is 4x larger, the MOT is rated at 6x the power rating so with all things being equal, a 1500w ballast transformer would be 24x the size of a MOT for the same rating. (that seems huge, maybe I'm off by a factor of 2, but I don't think so by weight...)

What's the deal with this difference

 

HID lamp ballasts are designed to run continuously for indefinite amounts of time while in severe environmental applications whereas microwave oven transformers are in short duty cycle and very mild working environments.

And no a 1500 HID ballast would not be 24x larger. It would be ~5 ~ 6x larger in mass and volume than a 250 watt one.