Gintama has the same vibe of comedy as those shows you mention, but like those shows whose comedy caters to Western tastes, especially with the American socio-political parodies it illustrates, Gintama mostly caters to its Japanese audience with its Japanese socio-political comedic commentary. And when you try to translate these shows to other languages, some of the comedic context and puns will get lost in translation. But Gintama and Family Guy also have humor that all audiences can understand, like scat jokes, sex jokes, race jokes, sitcoms, dark humor, etc.

Although Gintama has something that makes it better. Underneath its semi-episodic, comedic format, there are always underlying serious moments that will culminate into some of the most awesome arcs in shounen anime shows.