Is there any difference between "a man with pride" and "a man of pride"?
Which one has the meaning closer to "a man who has pride"?
'Have', 'with' and 'of' are sometimes synonymous. 'Man with pride' means that the man and pride are near each other, while 'man of pride' means that pride possesses the man. Since pride is abstract (irrealis) and the man is a physical object, neither literal meaning makes sense, so they are both taken to mean that 'the man has pride'. There is nuance in 'man of pride' that makes it stronger, since pride possesses him instead of just him possessing some pride.
I think the phrase you're after is "a prideful man".
Though the phrase is often used in conjunction with a negative connotation you can employ context to avoid that.