Australian sandalwood has the same chemicals but in different proportions. The level of santalol is alot lower, for one thing. Desciriptions I've read say that the Australian wood is drier and less sweet. I've never smelled Mysore sandalwood, but have smelled Australian sandalwood. To my nose it is a drier, woody smell as compared to the synthetics which seem warmer and sweeter.
Most fragrances now days use synthetics for sandalwood. Alot of the Australian sandalwood is sold for incense and aromatherapy purposes. It's also not exactly cheap stuff as far as essential oils go.