I would say that "stubborn" has a negative sound to it. There is a saying " stubborn as a mule" which visually isn't very flattering :) Also, I think that stubborn is used more often than "adamant", even though the meaning is almost the same. Someone can be adamant about something and that stance wouldn't necessarily be looked upon as bad. An example of stubborn would be: She is too stubborn for her own good. (She can't see that her decision is a bad one...) An example of adamant would be: He is adamant about pursuing a career in acting. (Maybe some people are ok with this and some are not. Depends on the conversation)

Priscilla was correct. Stubborn is definitely more negative. Stubborn is also used to describe a personality type, which is what Priscilla's first example is saying. You could describe someone as being stubborn, but you would not say 'She is an adamant person'. I guess that is because being adamant is something occasional, but being stubborn is describing something habitual. He is a stubborn person. Dad is being stubborn about moving to a retirement home. He is adamant that he will not get his car stuck this time.

"Firm" is a short, everyday word with a positive connotation. Someone "firm" has taken a good position and is going to stick to it, possibly because it is right, sensible, wise. "He said no." "Can you get him to change his mind?" "No, it was a firm denial." "She is a woman of firm convictions. She persists until she reaches her goal." "Adamant" is much rarer, and more "literary." It means "firm" or "very firm" or "absolutely firm." (Literally, "adamant" is another form of the word "diamond," the hardest substance in the world). "Stubborn" refers to someone who won't change their mind, never changes their mind, even when they are being wrong or stupid. "He's a very stubborn person, once he makes up his mind he won't listen to anything." "Stubborn" can also be used about things that are difficult to move. "The lug nuts were rusty. I was able to loosen four of them, but the fifth was so stubborn I couldn't do it." "Obstinate" means the same thing as "stubborn." There is an informal, insulting term "pigheaded," which is even more negative than "stubborn."