Difference between "meant to" and "supposed to"
Solution 1:
They are freely interchangeable in many everyday contexts, but there are differences in the tone of voice. "Meant to" has a more philosophical, fatalistic connotation, while "supposed to" might refer to a transgression or snafu of some sort. For example:
Despite the best efforts of the director, the actors and the rest of the crew, the movie didn't do well- it just wasn't meant to be a blockbuster. Try substituting 'supposed to' here and it sounds way wonky.
Despite the best efforts of the director, the actors and the rest of the crew, the movie didn't do well- it just wasn't supposed to be a blockbuster. Well, what can I say. It was supposed to be a blockbuster; unfortunately, it wasn't meant to become one.
So, my submission is, the context matters. 'Meant to' might be used in situations that can be remedied as well as in situations that can't, while 'supposed to' might be used in a situation that can possibly be reversed.
Solution 2:
As far as what they mean, they are fairly similar. The connotations of the two words, however, differ slightly. "He is not meant to do this" implies a plan or design where the intent is not that he do it. "He is not supposed to do this" implies an expectation or understanding, and seems to come from a more observational standpoint, whereas the first seems to come from a standpoint more knowledgeable about some plan involving the subject and his actions.
Actual definitions:
to mean:
a : to have in the mind as a purpose : intend she means to win
to suppose:
(2) : to think probable or in keeping with the facts seems reasonable to suppose that he would profit
Solution 3:
Thursagen's answer is right, but I wanted to expand:
1) I think that "meant to" is a bit more formal. "He's supposed to..." strikes as extremely informal and I would keep "supposed to" out of formal writing. Likewise, 'meant to' seems rather off in informal conversation. That said, I think that both of these phrases are rather casual and you would generally use another phrase in writing anyway.
Take this conversation:
He's supposed to make sure the printer is working!
He's meant to make sure the printer is working! <-- weird
Take this piece of writing:
He is supposed to implement this feature by December 2011. <-- Too informal
He is meant to implement this feature by December 2011. <-- Good
He intends to implement this feature by December 2011. <-- Better
2) "Supposed to" always implies that there exists a definitive set of steps that someone could potentially take to accomplish something. This is not always the case for how "meant to" is used.
You might say:
He's meant to end the war.
He is not meant to follow this path.