It depends on your climate and which herbs you are growing. A lot of them originate from warm sunny countries, so if you live in a very cold damp climate then they may be better off indoors.
However, the perennial shrubby herbs, such as sage, rosemary, lavender etc will probably do much better in the ground outdoors where they can grow unrestricted.
Smaller and annual herbs are more suitable for growing indoors - I nearly always have a pot of basil on my kitchen windowsill as it seems to do better there. When growing indoors you have the added bonus of being able to extend the growing season. Here in England I usually bring a pot of mint indoors to bring it on early in time to go with the new potatoes out of the garden.
The disadvantage of growing indoors is the restriction of pots on the size of the plants, and also that they need more care than outdoor plants in the ground.