According to me, active RFID tags are more likely to suffer from a security attack (i.e. the risk is higher) than passive tags because active tags manifest their presence themselves in their neighbourhood without needing that the reader provides them energy. However, my teacher did not agree with me and couldn't see an a priori difference in the security risk between passive and active tags. Could someone argue if there is or is not a difference?
As you have not specified a threat model, I'll assume the most common one for RFID tags: cloning of the RFID tag when used for access control.
In that case, merely being an active tag does not make it more or less risky than a passive tag. A sufficiently powerful active tag might have a longer read range, making it easier to clone at a distance, but both would be a relatively short distance (e.g., meters at most) and would not make it substantially easier. Active tags (self-powered) are also often able to have a more powerful microcontroller, offering more options for encrypted RFID communications, which might make them more secure.
Without anything more than "active vs passive" to compare, there does not seem to be a meaningful security difference.