Part of it can be explained by different gene expression regulation modes: Prokaryotic gene expression is mainly regulated on transcriptional level, which is only possible with short mRNA half-life times. Only when an RNA is unstable its accumulation depends on transcription. Eukaryotic gene expression is much more often regulated on translational level, which is only possible when the mRNAs are stable. Only stable mRNAs can be activated/deactivated by translation. If they would be unstable the regulation mode would switch back to transcriptional regulation.

I believe it party has to do with how it is translated. For a eukaryotic organism, it must be transported out of the nucleus and into the cytoplasm where it can bind with a ribosome, where as there is not nucleus for prokaryotic bacteria. For prokaryotic bacteria, it can be immediately translated, and often gets translated as it is being transcribed.

Part of it can be explained by different gene expression regulation modes: Prokaryotic gene expression is mainly regulated on transcriptional level, which is only possible with short mRNA half-life times. Only when an RNA is unstable its accumulation depends on transcription. Eukaryotic gene expression is much more often regulated on translational level, which is only possible when the mRNAs are stable. Only stable mRNAs can be activated/deactivated by translation. If they would be unstable the regulation mode would switch back to transcriptional regulation.

This is a very interesting question, my input is as follows: technically there should be no difference between the two mRNA as inherently mRNAs (like all other RNAs) are polyionic molecules and they clasps quickly to form ‘self-helix’ or a hairpins; so the question of stability could lie in the size of the mRNA molecule and the type of series of bases they may contain; the longer the mRNA (as in the case of eukaryotic mRNA) the less stable it will be in cytoplasm; moreover, it is perhaps as well that eukaryotic mRNA is transported from the nucleus to the site of translation (ie 80S ribosomes) via the nuclear pore and the endoplasmic reticulum. The prokaryotic mRNA being typically smaller than eukaryotic and which is, in general, being translated (by 70S ribosomes) as it is being transcribed is, perhaps, appears to be not so important.