T4, or levothyroxine, is actually the reserve form of T3, or liothyronine. The thyroid secretes the majority of its hormone as T4. T4 is the less active form of thyroid hormone, and gets metabolized into T3, by the removal of 1 iodine atom...T4 - 1 Iodine = T3.
T3 is the active form of thyroid hormone in the body, actually 5 times more active than T4. This is the agent that actually causes all of the major effects: metabolic elevations, thermogenesis, cardiac stimulation, etc.
In terms of use, T3 has a much shorter life in the body, around 1-2 days, while T4 has around 7 days. This is why doctors prefer to give patients T4...it is easier to control. Just give the patient some T4 and the body does the rest (the body decides to activate it as it sees fit), whereas T3 is active and can be tricky to get just right.