In the treatment of hypothyroidism, thyroxine is preferred over liothyronine because of thyroxine:
Liothyronine (T3) as compared to thyroxine (T4) is:

Fast acting
More potent
Short half-life

An indication of liothyronine includes myxedema coma and for most of the indications, thyroxine is used because it has a long half-life thus can be used less frequently than T3.
Is faster acting
Has higher affinity for thyroid hormone receptors
Has a longer half life
Can be made more easily by recombinant DNA technology