There are advantages for having tanalised garden sheds, but there are also a lot of disadvantages too.  When timber goes to be tanalised or pressure impregnated, all the moisture is taken out of the timber and supposably replaced with the tanalising preservative.  You will find that once you cut into the timbers, the preservative DOES NOT full penetrate into the timbers therefore leaving bear timber open to the elements.  This is the main disadvantage to tanalised timbers. 

From our experience, it is much better to use a good quality spirit based timber preservative once the building has been made, the furher treatments once every 12 months ideally before winter.