What's the difference between "You have my word" and "I promise"?

Solution 1:

There's not a lot of difference. However, "You have my word" could be construed to imply that you have previously (already) promised (given your word) and this statement is a reaffirmation of what was said before, whereas "I promise" implies that you are just now giving your word. OTOH, "You have my word" could be taken as present tense too, and would then essentially be the same thing as "I promise".

Solution 2:

There is really no difference. It can be argued that "You have my word" is a bit stronger, because "my word" means the person is taking an oath, in effect guaranteeing based on that person's honor, but that is a very fine point indeed. A promise means the same thing:

promise: a declaration or assurance that one will do a particular thing or that guarantees that a particular thing will happen

one's word: a promise or assurance

So one's word is a promise. No difference.