Hydroponics have their pros and cons. While it has been reported to offer bigger yields, in some plants, the quality of flavor lowers somewhat, depending upon the nutrients used in the solutions. There are several hydroponic applications out there, so my advise would be to talk to a place that deals with those systems and ask them about growing herbs with them. Also keep in mind your requirements and your limitations, such as space limitations, costs of operation (nutrients, water, electricity), and time.
Some systems require a bit of room and control of the solution which is used to feed the plants, since most times hydroponics use a soil less growing medium such as clay pellets. Another issue is that many require electricity to control the pumps and irrigation of the crops, and if you have power outages, this can cause problems to root systems if you are unable to provide the water and nutrients during that period.
Basically, you manage everything in your plants growth cycle and the nutrients it receives. If this is something you feel you would enjoy then go for it, though keep in mind the above factors. If you're only wanting a small herb garden then I suggest a raised bed or a few pots with quality soil. You can use drip irrigation or simply water by hand.
Talk to a nursery that deals with hydroponic systems to discuss your needs and see if it's right for you. Personally, things in the dirt simple taste better to me, but to each their own. Hope this was helpful and best of luck to you.