Well I consider what makes "the individual" that is me the composition that makes up the brain and body I have. If you can recreate that composition I consider both people to equally have my individual point of view.
The opposite scenario is that there are now two consciousnesses. If the original dies so does its consciousness and you failed to achieve immortality. Your clone is just your offspring with an identical body and set of memories.
So which is it? I personally picked it based on what I want to believe in, because even if it is a lie it helps me shape the world into one in which I want to life in, rather than one that I do not like and would prefer to get rid of.