Why are adult stem cells not more likely to be rejected by the patient's body than embryonic stem cells.
It's because they have specialised and have developed distinct markers that identify them as non self to the host immune system. Embryonic stem cells don't have this specialisation, they can be easily integrated in a transplant. In fact, due to their tendencies to grow and proliferate, embryonic stem cell transplants are plagued by the problem of too much growth to the degree that it will cause a malignant tumour
Adult stem cells are found scattered in different places that may be hard to reach eg bone marrow whereas you can just grow a ball of embryonic stem cells if ethical guidlines permit it.