Purple basils are just cultivars from common basil - there are quite a few. They can be used in the same ways as common basil (ie. they're edible as well as pretty enough to be ornamental). They've been designed for the colour, and occasionally the flavour has suffered in the process, but I've found the flavour pretty much the same. Depending on the cultivar, the plant will often revert to green. One way to prevent this is to remove any green shoots as soon as they appear. If left to its own devices, such a plant will eventually become all green.

The flavour of plants such as basil (purple or otherwise) comes from the essential oils which the plant produces. In the case of basil, the more heat and sunlight you give the plant, the more of those essential oils will be produced. A plant with non-green leaves may have to work harder at it. So if you're in a relatively cool area, the flavour won't be as strong as if you live in a hot area with long hours of strong sunlight. I'm in the subtropics, so have no problems in that area!!

There is one purple basil, smells good, it is a vaiety of Krishna tulasi(holy basil).It is sold at seeds of India.com.
It is an anual, I am not sure whether it is edible, I grow them as companion plants for tomatoes along with marigold.

Holy (Sacred) Basil is edible. Not to everybody's taste, though!