The ATC wind is taken from a device that directly measures the wind velocity and designed specifically for that purpose. The FMC wind comes from a calculation involving ground speed, heading, track, and true air speed and is not a direct measurement of the wind. Further, two FMCs in the same aircraft may differ by a few knots in calculated wind. Given the above, I would take the reported wind as gospel and the FMC wind as of academic interest only provided it is relatively close to the reported wind. Additionally the flight manual for the type I'm familiar with states that winds are factored such that a tail wind accounts for not less than 150% of the tail wind, head wind accounts for not more than 50% of the head wind and "reported winds may therefore be used directly".