I have migrated my website from Joomla to RubyOnRails, but, I've noticed that number of likes has changed at the same URL!
It was about 780 in the old website, then it became 35 in the new one
What possible reasons it could be?
The most likely reason would be that the URLs are not exactly the same. Most likely due to a query string at the end of the URL.
If you are positive that isn't it, check to see that the source for calling the facebook like button is the same.
This is a long shot, but if it still isn't fixed, you might want to compare the meta data inside the head tag and look for differences there.
<link rel="canonical" href="http://my.website.com" />
would be one that comes to mind.