You can use majestic SEO to check for backlinks on a range of criteria - this is what MNF will be using once yahoo site explorer closes. The link is here; https://www.majesticseo.com/
Every tool will give slightly different answers. The best thing to do is to take an average of the 2.
When I use backlinkwatch.com I get far less then when I use backlinkchecker.com Wish the results were more streamlined & accurate
Try Google web master tools, it provide you exact numbers not only about the inner links and also sites linking with yours.