I like Earthbound's kookiness and obviously it's a matter of taste but personally I feel like the story, both in and out of game concerning Terranigma is really incredible.
I mean, on the outside, the developer for Terranigma was actually depressed. This was after Terranigma's spiritual predecessors. Anyway, apparently he met a man in strange clothing who was traveling around the world, who helped the guy out of his depression, thus it was this that inspired him to make Terranigma, the third and final installment to the spiritual series (I can't remember the first one but the second is Illusion of Gaia).
But the reason the inside story works better for me is so: Earthbound has a great story. It's direct and not direct at the same time and it twists and turns and has some emotional, kooky and hilarious moments throughout the story. HOWEVER, once you've defeated giygas, that's pretty much it, you know what's happened, you know the meaning of what you've done.
In Terranigma, your story is indirect, you have no idea what you are truly setting out to do. Then you resurrect the world and things get further tangled as you enter first through the world of plants and animals, to the world of humans, villages and the first planes and all that. However, through all of you've got these tasks that give hints of what the real evil is. Then... you have that whole deception thing and I won't even go in to that because that's an integral part of the story that is seriously heart-burning and it leads on until the end...
And through everything, all you've ever wanted to do is be with Elle. That's it, nothing more. But there are worlds between you and still you're unsure of your true being. Then, at the very end... well, everything there is open to interpretation and it's also integral to the story so I won't spoil it for tik.
Basically what I love in Terranigma compared to Earthbound is that it really makes you think, from start to finish, think about life and though many sad things happen, it gives you this optimistic outlook on life. I really do love Terranigma, it is my favourite game of all time and IMO it just does everything right. Earthbound does too, there's just differing degrees of success. ^_^
Also, my favourite VGM of all time comes from it, I doubt you will have heard it because it's at the end of the game, in the epilogue. It's... so sad and so beautiful... don't listen to it unless you've played the game because even its name is revealing! :o