Is It Always Quicker To Use A Microwave?

Nearly always, but there are exceptions. Rice and dried pasta need to have water added and to rehydrate, so they take about as long in a microwave as in a saucepan. Slow-cooked meat dishes, like casseroles, are also no quicker in a microwave as they the meat needs time to break down and tenderise. Also, in practice some packet dishes, e.g. bread sauce, aren't much quicker as you have to allow them to stand after, and stir during, cooking.
Nevertheless, the vast majority of ingredients do cook quicker –though not always better –in a microwave. They are especially efficient if you remember to cut things up small, putting the thinner pieces towards the centre of the dish. A thin, microwaveable plastic dish will cook ingredients more quickly than a heavier oven-type baking dish, even if the latter is microwave-safe. Also, don't overfill your dish –rapid cooking can result in overflow.