The E string is not a wound string (with a softer core) so it just does not have the same failure modes as other strings. How much the G string gets played depends also on how likely you are to play in higher positions (which leaves more material in the reach of the G string).
Generally the G string on a violin has less of a tonal substance and resonance than the G string on a viola, so it tends to see less action. There are some exceptions: Monti's "Czardas" comes to mind with its initial passage to be completely played on the G string: that's sort of a romantic excess. In practice, this tends do deliver a consistent but slightly "hoarse" rendition though the details depend on both instrument and string set.
In orchestra use, the G string tessitura tends to be more prominently covered by violas, with violins only making occasional excursions into a range which the build of the instrument tends not to support with as rich a resonance as the large body of a viola could.
Solistic use tends to see more of G string action, and of course when playing folk music, the use of G as a drone string providing harmonic support (fingered or unfingered) below the actual melody line is actually rather common.
But all in all, this is so much an outcome of the chosen repertoire and composition style, that the proper answer is "it depends".