The accuracy specification indicates that your measurement will fall within a certain value of the actual voltage, and takes into account factors such as noise, temperature drift, and gain and offset errors on the A/D converter. The resolution specification (number of bits) does not affect accuracy directly, but indicates what discrete values you can measure. Both boards have the same accuracy specifications (so the measurements will fall into the same range), but the resolution of the input signal will be four times greater on the 6009.
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