For the record:
First, a repository is a backup then later its about security.
To the date, we are yet to see a security breach that involves GitHub or Bitbucket. So, empirically speaking, they are safe.
However, we are showing our information to a private company, so there is a risk, for example a Github employee that decides to copy our stuff.
But, we should remember that a repository is mainly a backup. Having a private server is fine if you own the resources. But, we should also consider the location of the server. If its in the same location then there is a chance of losses all the information, for example a flood, fire, a thunderbolt frying all our machines and so on. So, a remote repository is really cool.
If you want to use a remote repository then, don't be too obvious. Lets say that you are Cocacola Corp and you want to manage an important project, then don't create a account with the name of the business and don't call the project as IMPORTANT_SECRET_VITAL_FOR_COCACOLA, just call it PROJECT1 and if a hackers attacks then he will not care about it.
