Having site with non www rank better or it is an illusion?

I think there is no such that having site with non www rank better. Just fix 301 redirection to set website with www or without www. Always fix this redirection issue because domain with or without www may look identical to human eyes but in the eye of search engine they are different domains with same content and that may harm.

There's no difference for ranking the www or non-www, so long as:

1. You be consistent with the version you build your backlinks to.

2. You set up a 301 redirect from the www to the non-www version or vice versa (you set your preferred version in GWT).

Hi,
If your site rank differently for www and without www then it might be caught by Google in future and considered as duplicate content. Your site requires a 301 redirect to overcome the issue.

No its not like that without www it can rank better long time it can even hurt you

I have never seen sites ranking better for non www.

For this I would like to say non- www is a bit better because old browsers can access non-www links.

If you have duplicate content from two different domain names then it will not work. The Canonical code only works with sub domain names from a single top level domain.The canonical URL is the search engine friendly URL that you want the search engines to treat as authoritative.