When the thought is "I'd like this person to know how grateful I am", the medium doesn't really matter.

When the thought is "I owe this person a 'Thank You'", the handwritten letter gives an illusion of deeper thought. That's why there are fonts designed to look handwritten. To the receiver, they're just junk mail. I'd rather not get them at all, in any form. I was happy just having done the thing, and the thoughtless response slightly lessens that joy.