What kind of emotions do you experience when you see or hear about someone experiencing a misfortune? What thoughts run through your mind? Many people believe that expressing sympathy will help the unfortunate soul feel better. The truth of the matter is that sympathy is very superficial. There is a deeper sentiment that, when expressed, indicates to the suffering party that you care on a higher level, that you may actually want to do more than present mere words of "I'm sorry" to them. Let's look at the difference between these two expressions.
Sympathy: to feel sorry for an individual; to express pity or sorrow for another's misfortune. You see, when we sympathize, we do express feelings for the individual, but we also reserve a little bit of relief for ourselves. It's the idea of "Man, it sucks to be you. Sorry dude. Thank goodness that's not me." We are not completely heartless in that we acknowledge the troubles another faces. But at the same time we are grateful we are not going through the same things. This creates a barrier between the sympathizer and the person in hardship. Many people who receive sympathy can intuitively, sometimes consciously, sense the superficiality of the sentiment. Rather than help them feel better, sometimes mere sympathy makes matters worse. Not many people like others to feel pity for them; it is a major blow to one's pride and self-esteem. Sympathy isn't all bad. Although superficial, it can convey some level of care between individuals, which is sometimes better than nothing at all.
Empathy: to feel the emotions of another; to understand the feelings of another person from their perspective. Empathy takes the notion of feeling for someone to the next level. You not only understand, on an intellectual level, how much emotion the person is experiencing, but you also feel it yourself. Your heart aches when they ache. You are sad when they are sad. Their tears of joy are reflected in your happiness. You know exactly what the pain, trouble, turmoil, etc. that they feel is because you either experienced it yourself or you are capable of putting yourself in their shoes and feeling it with them, from their perspective. With empathy, there is no sentiment of "Glad it's not me." Instead, because you feel what the other person feels, you may become swept up in their emotions. You are also more likely to help them. After all, if you feel their pain, then lessening it for them will reduce it for you. With sympathy, you are free to walk away and let others solve their own problems while you get to look like a good guy for doing nothing. With empathy, you are in the middle of the mix so you not only get the dark side, but you also get to revel in the light side when things improve.
You can see the distinction between an empath and a sympath in the characters of Deanna Troi (Star Trek the Next Generation) and Emma Frost (Marvel comics). Counselor Troi, especially in the first couple seasons of TNG, not only sensed the emotions of others around her, she was sometimes overwhelmed by them. This could occasionally lead to emotional overload for her if the feelings were especially strong. With this empathic ability, she was just the right person to fill the role of counselor, as she would be highly motivated to help others heal and find happiness. Emma, on the other hand, was able to detect the emotions of others but she rarely lost her calm demeanor. She typically kept outside the emotional realm of others around her, creating a barrier between her own emotions and those of others. She knew what others felt, but she did not experience it directly herself. In this way she was able to manipulate others around her without losing control of herself, giving her the upper hand and allowing her to rise to power or hide away when she needed to.
Is there anything wrong with sympathy? Not really. But know that empathy--to truly feel what others feel and not just because you want to win the "my life sucks" game--is more helpful in the long-run, though it may be a bit more draining on you than sympathy.