Basically the difference between sympathy and empathy. You can validate someone's feelings by simply acknowledging them (sympathy, "I'm sorry you feel upset about that, how can I help?"), or you can participate in that emotion (empathy, "Yeah, that pisses me off too! Let's fix it.").

Neither is definitively better or worse, sincerity is paramount, and it's all contextual, including the personality of the person involved. I think aligning on what mix to use is possibly the most important thing in a relationship, especially a professional one.