Regularly pilots ask me about the use of the FMS wind vector. I have written a number of articles that give some background information on this topic. A number of them have been quoted in this forum before. Let me try to share some of my thoughts about this topic.
The FMS wind is not what it appears to be, in particular during takeoff and landing. First, the FMS wind is not corrected to a height of 10 meters. At 500 ft. AGL the wind is about 50% higher than at a height of 10 meters. If the FCOM/AOM gives you a tailwind limit of 10 kts. it applies to this 10 meters AGL (just like the crosswind). The tower wind is normally (but not always!) measured at 10 meters for that reason. Second, internal FMS calculation of especially the crosswind component during approach is filtered, delayed and very sensitive for small errors in track or heading measurement. Furthermore, the FMS wind is not corrected for sideslip. It is true that the FMS tailwind component is relatively insensitive to FMS errors in the determination of the drift angle. However, the problem of an incorrect/inaccurate FMS tailwind does remain due to the height influence and the processing delays. So what should you do when you get a tower report just before landing which significantly differs from the FMS wind vector? The save answer I can give is always to follow the procedure in the FCOM/AOM. This usually will not state that you should use the FMS wind to crosscheck the reported tower wind. At least I am not aware of operators that formally state to use the FMS wind during landing.
On the other hand some airports do not measure the wind accurately. If you believe that this is the case you should report this to your safety department or flight ops department so that they can contact the airport/authorities to take the appropriate actions to solve this problem. And yes, I do realise that in some regions this is a challenging and difficult process.
Some additional reading:
Wind at Your Back - The Hidden Dangers of Tailwind
Aviation Safety Letter 1/2005
Crosswind Certification - How does it affect you?
www.nlr.nl/id~5114/lang~en.pdf
Safety aspects of tailwind operations Safety aspects of tailwind
www.nlr.nl/id~4359/l~en.pdf
Safety aspects of aircraft operations in crosswind
www.nlr.nl/id~4382/l~en.pdf