Honestly, besides being from the 90' and both being about alien invasions, the two movies have nothing in common and obviously had pretty different goals.
Mars Attacks was meant to poke fun at absurd science fiction from the 50's, the ignorance of the world's leaders and the disaster movie stereotypes is done on purpose to illustrate just how ridiculous those movies were. Some of the cast members seem pretty aware that they're in a comedy, while others play it very straight like in Airplane.
Independence Day on the other hand was meant to function as a modern re-interpretation of 70's mainstream disaster epics and science fiction so its plays it more straight forward. There's satire, but it's more hi and bye. Comedy is in there as well, but it's all reactionary and not the dominant tone of the story.
Interestingly enough, the original Mars Attacks merchandise depicted the aliens and their invasion of Earth to be very dark and graphic, if the movie went for the same kind of tone as Independence Day, kept the 1960's setting, and kept the same graphic imagery of the Topps cards with a director like Paul Veroheven at the helm it could've been a really trippy flick...But I think the movie is fine as is, though I do wish Burton didn't go for a modern setting if he really wanted to push the satire a bit further.
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