People renounce different things and different systems of spirituality require different types of renunciation. Renunciation is a really important practice in both Christianity and Buddhism but the most important thing to understand is that it doesn't matter what you renounce. The real goal of renunciation is not to renounce different types of behaviours or thoughts. The real purpose is to renounce what underlies all of them. However, this underlying factor is very subtle and it is difficult to get direct experience of in its pure form, uncoupled from specific desires. It is far far stronger than any specific desire in its pure form and it cannot be overcome by any act of will. Using will to renounce specific things is useful to gain insight but also dangerous because the use of will must ultimately be abandoned. If it is not then the desire to use will will replace whatever desire has been renounced and the situation will be much worse. Historically, this appears to have been a dangerous trap for well meaning monks.