Yeah, Mother 3 (Luca's game) was a lot more serious than Earthbound. It had more tragedy and a lot of the stuff in it was genuinely sad. Lucas is actually quite a psychologically disturbed little boy. The story in general seemed to be deeper and a lot of the attempted humor still had a kind of seriousness to it that didn't make it quite as funny as anything found in Earthbound.
*FRIKKIN SPOILER WARNING ON REQUEST OF LAHA...I MEAN ADEMISK*
For example, there's a point in Mother 3 where Lucas learns how to use PSI from the Magypsies, who are basically a tribe of cross-dressing men with magic powers. He ends up going into a hot tub with one of them and having his head dunked under water to awaken his abilities. However, the way the screen goes dark, the dailogue and an event later on where Lucas reveals through a hallucination that he's afraid of sexual situations could also mean that he was abused. It's a mild topic of debate amongst Mother 3 fans or so I've been told. But yeah, Mother 3 has a lot more subtle adult undertones than Earthbound.
Lucas also had a lot more character development in Mother 3 than Ness did in Earthbound, which goes to explain how they act in SSE. In SSE Lucas displays some of the timidness that he had at the start of Mother 3 before he had any friends to help him. Ness, however, is shown as being a heroic and fearless character, since in Earthbound he was basically an unstoppable robot who never dropped his smile, even when facing the greatest evil of all.
*END FRIKKIN SPOILERZ.*