When I hear someone says "I apologize for..." to me it sounds that they've really given it some thought and regret what they did. Where as I'm sorry is less sincere
Most Helpful Guy
I think that to someone you hardly know, especially if it's a superior, or a customer, you'd rather say "please accept my apologies" or "I would like to apologize for...".
Whereas to someone you already know you'd simply say "I'm sorry for my mistake".0