The weapons the costumed Inklings are shown holding are the weapons used in the single-player missions that unlock them, which probably (it isn't a gameplay screenshot, maybe the devs just made the picture that way so it would look cooler) means the amiibos unlock those weapons for multiplayer. I highly doubt that there will be any weapons that are straight up stronger versions of others, especially not amiibo exclusive weapons (that would be ridiculously unfair).
The amiibo weapons could be functionally different from other weapons but still balanced so that none are blatantly the best, or they could be reskins. I personally find reskins more likely.
