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When I open a layer projected in ArcGIS with EPSG:25831, QGIS detect it as EPSG:3043.

Apparently everything is where it is supposed to be, and checking both EPSG:25831 and EPSG:3043 they appear to have the same bounds.

Is there any reason why QGIS deals with this info as 3043 or it is a bug? Is it possible that not changing it to 25831 can cause my data to be imprecise?

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    The difference between the two is that when using EPSG:3043, interchange data should be give in northing,easting order rather than the usual-for-UTM order of easting,northing, as in EPSG:25831. – mkennedy Jan 12 '17 at 19:23
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IMHO,the projection parameters are the same for both codes:

+proj=utm +zone=31 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs

Important is the contents of the * prj file. If it contains only the parameters and not EPSG code self, QGIS uses the first suitable parameter entry.

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