Both Armageddon and The Core are stupid and silly. The comparison in and of itself is pretty stupid and silly, but trying to argue that one is better than the other?
As for Armageddon OR The Core EVER taking themselves seriously...uhhhhh, no.
Armageddon isn't more serious - it's more melodramatic. I'm not sure how many fake tears Affleck and Willis needed for their "goodbye" scene, but I understand they ordered in bulk. And then Bruce did it again saying goodbye to Liv. Not serious, but pretty clearly going for misty eyes with no apologies and no subtlety. Add to that the WONDERFUL (turn on your sarcasm meter) love story with Liv/Ben, or even the hilarious "reunion" of Will Patton and his son or the POWERFUL strains of the Trevor Rabin score...and you have hambone city.
The Core plays it only slightly different - less tears, more opportunities for heroics, etc. But, anyone who sees it as taking itself seriously isn't watching the same movie as I saw. "Unobtanium"? Tucci at his hammiest (and having one HELL of a fun time)? Torching a peach? Wild birds causing ridiculous havoc?
Two silly movies, two fun times. I saw Armageddon at a special midnight preview. A blast. I saw the Core at a packed late night Hollywood showing. A great time.
I will never watch either again unless I'm really tired, really bored, really lonely, AND really desperate.