There's really not much out there, because the chemistry of instant film is very difficult and without the film, there are no cameras. Fuji's only real competitor is The Impossible Project, now known as Polaroid, having bought the name. Their cameras are very nice, but their film is more expensive and technically inferior (though not necessarily aesthetically inferior, depending on your goals.) You can also buy film from them that is compatible with classic Polaroid cameras.
Polaroid has always been worse than Fuji from a technical aspect, but that's always been part of the draw, I feel. It's why Instagram got popular in the first place as the filters mimicked the colors of a washed-out Polaroid still from various decades.
