The correct statement regarding a difference between gene regulation in prokaryotes and eukaryotes is:
Prokaryotes do not store their genes in a nucleus like eukaryotes do.
This is a fundamental distinction, as prokaryotic cells (like bacteria) do not have a membrane-bound nucleus, allowing for simpler and more rapid gene regulation directly in the cytoplasm. In contrast, eukaryotic cells have a defined nucleus where transcription occurs, followed by a more complex process of mRNA processing before translation in the cytoplasm.
The other statements mentioned contain inaccuracies or simplifications. For instance, eukaryotes do not "transcribe genes randomly," they also respond to environmental stimuli; and not all eukaryotes organize their genes into operons, while prokaryotes often do.