The kind of sharing you are referring to, requires your brothers HOME xbox to be the one you are playing from and vice versa.
SO if you have 2 Xboxes and 2 Accounts:
Your brothers home console needs to be your xbox, where you then log in with your account to play on.
Your home console needs to be on your brothers xbox, where he is then logged in with his profile, still able to play your games.
This way is how i have been using it for the past 3 years without any issues.
The important step is to make sure you set each others Home Console on the other persons Xbox, to ensure he has access to the content, even tho he is not logged in.
Hope this clears things up.
I'd say if you're worried about privacy issues, deleting your profiles from the console should be enough.
But, to clean out the storage space, you should go to Settings > Manage Storage and then delete all game data, including saves. You could alternatively delete local saves from the same Settings menu, one button down.
Then, just to be safe, you could restore factory defaults, the next button down in that same Settings category.
That will remove your games, your saves, and your profiles. Even if you just deleted your profiles though, your games and saved games would be inaccessible to a new owner without your gamertag and password.
Also, your data should sync to the new xbox one when you enter your profile data the first time. Id do some research though on games with saves that you really value, in case some games dont support that feature for some reason.
Best Answer
You can do so from the Account option in the settings as described here (second option under "Topics"). Keep in mind that if the accounts are secured by a password, you may need to provide it to be able to remove the account.
Removing accounts that are valid Xbox Live accounts will just remove them from the console, not delete them.