Is saving a private key encrypted with the users password safer than storing a hash in a database?

Is storing a private key generated by the client that is encrypted by the users password safer than storing a hash of a password? (The encryption part is done client side and it will be sent to the server the users password won't be sent to the server)

It depends what you're talking about.

If i'm the client:

• i generate a pure random "key":
  58 3b ae a9 de 37 88 e6 ed a2 9f 45 db 8b 9f 56 ef e1 aa 25 ac 52 f6 3d 02 dd 1b 86 1f c5 39 44
• i encrypt it with a password: 3e 35 33 46 fe a2 04 09 58 ff 1a 29 41 97 cb 6d 44 32 5f 4a 74 01 90 1d f3 32 eb 2c 6e 49 e1 19

What you've done is have the client create a strong password with extra steps. I can convert those bytes to a string:

4uG,crh9N%=T99g6'oc36o&+AF9.IDo.oV_DFre)

This is now the user's "password". When they login to your site, you need to validate that password. That means that you must securely store that password in your system - and taking the SHA-256 hash of that password is not secure.

That's all if the client encrypts it

What if instead the user generates a "private key":

58 3b ae a9 de 37 88 e6 ed a2 9f 45 db 8b 9f 56 ef e1 aa 25 ac 52 f6 3d 02 dd 1b 86 1f c5 39 44

And they send that to the server, and you will encrypt it with the user's password: how did you know the user's password!?

You can't do that, because you can't know their password.