Delete

08:06 Aug 14, 2014 

Of course, I agree. Some UI's use "ukloni" for delete, but there's "remove" for that...
Although we cannot thoroughly delete data, we still can "delete from profile", "delete comment" and things like that.
So your vote goes for izbrisati, izbriši.

07:57 Aug 14, 2014 

My personal "feel" for this matter is that effectively "obrisati" should be used for "obrisati prašinu" or "obrisati mrlju / fleku" and "izbrisati" for "to delete data" (pictures, documents, whatever...)
But there is an additional twist to your question.
In most IT systems and on most websites with user-participation when users or sysadmin/webmasters/moderators "delete" something in actual facts it's NOT deleted, it's just made unavailable, impossible to access for ordinary users.
But it's still on your computer or on the website's server, and CAN be found and retrieved with the right software or access rights.
To make it disappear from your computer, it's not enough to "empty the recycle bin", you need software that can "wipe" files and even that is not perfect.
To make really disappear something you posted on the Web you need - nothing. You can't.