I don't know about an empathy gap - people's politics don't make them decent or not - but I do know that there's a definite "confidence" gap between liberals and conservatives. Conservatives believe in the unlimited ability of individuals to work hard and thrive, building a life for themselves and the people they love, while liberals believe that individuals are at the mercy of fate, through no fault of their own, and must be saved by the hand of big government. That is the biggest difference between conservatives and liberals - conservatives believe in the greatness of people and liberals believe in the greatness of government.
A Canadian conservative is one who believes in limited government and that the government should stay out of our wallets and out of our bedrooms.
"Obamacare delenda est"
Republicans, or more rightly conservatives, are more empathetic because all evidence points to the vast majority of voluntary charitable giving comes from conservatives. Conservative policies also are aimed at lifting the whole person, body and soul, not just limited to providing for temporary needs.
There is and that's a good thing. Empathy is not something that we want in politics. Sympathy is. We can understand that people have problems and we can be sorry that they do. We should not be putting ourselves into their places and finding out what they want because we're trying to feel what they feel. Empathy is a net negative.