what is the difference between installing bitbucket server in my local and hosting it in bitbucket site

[Daniel Wester]

Depends on what you're after.

If you're ok with hosting your repository in the cloud (and Bitbucket does have security stuff) and are team focused(even if it's a team of 1) then Bitbucket.org might be good for you. 

If you're a large company and are looking for repository hosting for all your development stuff then you might want to look at hosting itself since the Featuresets on Server will be more targeted towards that. 

In short - take a look at both. They're not exactly equal (close but not quite).