I absolutely adore the design of the North American SNES, its probably my favorite looking console of all time. The JP/EU version is.... okay I guess. Really this is no contest for me and I'm continually shocked to be in the minority on this.
The North American controller looks better too, I think, but JP is more comfortable and has the added gameplay of each button being associated with a different color. The rainbow buttons might look generic, they're the type of thing you'd see Spongebob using with his "Gamebox" or whatever, I'd gladly take usefulness of ascetics. NA's inverted X and Y were supposedly there to tell your fingers whether you were on A/B or X/Y but really even as a kid who ever messed that up? A useless feature...
Box doesn't really matter to me, JP is more artsy but thats not always a good thing, NA version is fine too. I'm just going to throw this out here at the same time- NA game boxes have a better style than EU ones, which just look like discount versions of the American packaging. Japan, of course, let companies put whatever they wanted on their boxes so there's some great ones and others that look like anime VHSes.
And as to the carts... I don't know how anyone could possibly chose the Japanese/EU versions, which are an all around pain to store. They lack top labels and are not flat so not only do you have the N64 problem of having to either custom label them or sort through every time, but the mere act of stacking more than three of them up on each other is an exercise in frustration unless you have some sort of nook to shove them into. If you only collect boxed or just have a couple this isn't a problem but if you have even a basic loose collection you'll quickly realize how obnoxious this is.