Swedish Massage - This is likely the most common type of massage, sometimes referred to as 'traditional massage.' It was developed by a Swedish doctor, Dr. Per Henrik Ling, in the 1820s, and is known as the first modern method of massage. Techniques include long gliding strokes, kneading, friction, tapping and shaking motions that affect the nerves, muscles and glands. It's ideal for relaxation, increasing circulation and energizing you.
Deep Tissue Massage - Targets the deeper layers of muscle and connective tissue. This is a deep massage meant to reach deep into your muscles and "unstick" the fibers they contain. This is done by deep muscle compression and putting friction along the grain of the muscle. It is especially good for muscle damage from an injury such as whiplash or back strain, and it helps release toxins and break patterns of tension.
Which is best? Depends on what you want in a massage.