Who said blogs aren't private? There is an option where you can keep the blog entire private or allow only your friends to read it - not the common readers. Then it becomes private, isn't it?
You have also an option to publish or not. As long a you do not click 'publish', the contents can be seen only by you.
In that case blog can be a better option because it remains lifelong
But once you are gone it is lost forever unless someone is able to retrieve your pass word and access it....As long as you want things to be kept that private it is fine but if you want certain things to remain for the next generation then diary is a better option....I was going through my mother in laws things and I have been reading her diaries since she was very methodical in writing down all the minute details.It is very interesting to read as well as giving many insights into her own personality and seeing things through her perspective...
The issue of 'diary or blog' is seen by some from privacy angle. So, if you write some thing only for your own pleasure and not wish others to see, blog is okay. also if you do not want privacy but wish to share, there are options for that also. You can manage privacy on blog/ social sites.