Different sites have their own metrics which they insert into the framework. FanGraphs and Baseball-reference are pretty close on everything except the fielding. So, if you see discrepancies between the two, it's usually because of fielding. Fielding is still hard to evaluate and is the biggest challenge in evalauting a player's overall contribution. The first thing I look at when a WAR seems too high or too low is fielding. If one stat says player A is a +10 fielder and another stat says he is a -5 fielder, that's a pretty big discrepancy (about 1.5 WAR difference). In that case, you have to decide for yourself whether or not you think he's a good fielder and choose the WAR that makes the most sense.