Getting an unsigned greeting card may not be a big deal for you, but it is for people such as Sir David Tang. The 60-year-old fashion tycoon, knight, and close friend of the Prince of Wales made the headlines in 2013 with singer and fellow knight Elton John over a Christmas card the latter failed to sign personally. Tang went so far as to consider John among "the common few."
Whether or not his reaction is justifiable, it just goes to show that many people value the thought and effort that goes into the making of a greeting card. You can have a printing company produce hundreds or thousands of copies of the same thing, but a personal signature can make a world of difference. The mere fact that you took the time to compose a brief but heartfelt message then signed the card personally will certainly not be lost on any perceptive recipient.
This, then, is the main value and connection that an authentic greeting card brings as opposed to cookie-cutter, generic electronic cards. Adding a brief, handwritten note aside from the default one greatly adds to the authentic, personal feel of whatever greeting you wish to convey to a colleague, a client, or a customer.