No, I do not think it should make a difference. Both of these positions are valuable in different ways, meaning that there will be various individuals who are interested in the position. Therefore, you need to set yourself apart and prove yourself as the best candidate whether or not the position is paid. This is done by mentioning your skills, past experience, life events, hobbies, talents, etc. Anything and everything that will help spark interest in the reader and improve your chances of being chosen.
