Difference Private Key Cryptography and Public Key Cryptography

Private/Secret key:

1. Private key is faster compared to public key
2. Private key is symmetrical. Actually, there is only one key. the other is a copy of it.
3. Private key is truly private. Should be available with only the two communicating parties. 
4. The two parties must have met before at least once to share the key.

Public key:

1. Relatively slow to encrypt/decrypt
2. Asymmetrical
3. Public key can be made public. Private key is truly secret.
4. The two parties need not have met. The two may be strangers, halfway around the globe.