Xbox 360 keeps telling me my password is wrong. And it isn't.

Coolio, now all I need is some XP and an Ambassador bobble hat.

Oh, and I am able to log in to that email and that password on my Xbox One perfectly ok.

If your password is longer than 16 characters you will need to make it less than 16 in order to play on your 360.

The password box on the 360 including the 360 emulator on the Ones is limited to 15 characters so if your password is longer than 15 it anything typed after that will not be seen by the system and it does not match your password that is on your account.

OK, getting the create app password for devices worked!

It could be you have two step verification enabled on the account, you can either turn that off or create an app password to use in place of your regular password.

https://support.xbox.com/my-account/security/turn-off-two-step-verification

or

1. Go to
   https://account.microsoft.com/security and sign in to your Microsoft account.
   
2. Select More security options.
   
3. Under App passwords, select Create a new app password. A new app password is generated and appears on your screen.
   
4. Enter this app password where you would enter your normal Microsoft account password.