I cannot tell exactly which one is accurate.
BacklinkWatch shows each and every links pointing to your site. Like, if you get a link from a blogspot blog homepage, BacklinkWatch watch will show links from all the pages of that blog. However, this link checker is slow that takes time to show your recent links.
In case of rank signal, it shows link from where it is pointed and not more than that. That may be the reason why no. of links shown by this site is low. And this tool can show your recent backlinks more faster.