IMHO, it depends on your requirements
Assuming you are asking because you want to select some choice for your home network.
Ethernet: If you want to stick to your working desk and a computer on top of it then Ethernet is sufficient. (Remember most of the ISP plans does come with a Ethernet port and cable).
So no additional money to be spent on anything. Quite stable connection.
Wireless: You want to use your notebook in Drawing Room, Bed Room, Living room or anywhere around your home. Ofcourse Wireless is required.
You need to invest some more money ( Buy a wireless router or get it from ISP), Connection is not as stable as Ethernet.
I dont want to talk about Security unless you are working for a secret agency ( If you are then I guess you dont need my opinions)