The two measurements appear to be in disagreement, and so the magnificent thing that is scientific debate is now ensuing on this question.
The 2003 observations would suggest, based on the believed lifetimes of methane in the atmosphere of Mars of several hundred years, that Curiosity should have detected it a 6 ppb. Curiosity has ruled out concentrations greater than 1.3 ppb. So either the original observation is wrong, or the lifetime of methane is wrong, or the models of how it distributes in the atmosphere are wrong. Or all of the above. This article provides an excellent summary.
As to why we care so much about methane, it is because it is one signature of life. Both extant life, in the form of, for example, cows on Earth or microbes on Mars (on Earth it's actually made by microbes in the cows), or even extinct life in the form of buried organics producing natural gas as it does on the Earth. Methane is not however a definitive signature, since there are abiotic geological processes that produce methane as well. But it would have been of great interest in the search for life on Mars to find methane in the atmosphere, since even several hundred years is incredibly fast in geological terms, indicating a nearly constant production of methane to maintain anything detectable in the atmosphere.