Is the public key more secure than private key?

The questions is not really which key is more secure - rather it is a question of "can you determine the private key if you know the public key?"

Public and private keys are associated with asymmetric cryptography. They are generated as a pair. The security comes from the difficulty in determining the private key if you already know the public key and have some cyphertext that the private key has been applied to or encrypting text with the public key and determining what key would be required to decrypt it. Since each key can be used to decrypt cyphertext encrypted with the other key using the same algorithm, there is not inherent reason to think that one key is more secure than the other. In reality, one of the keys will be numerically a better starting point than the other when it comes to executing an attack on the encryption and deriving the other key. In practical terms, however, an attacker is always trying to start with the public key and discover the private key, without which messages encrypted with the public key cannot be decrypted (or without which the attacker cannot impersonate the holder of the private key).