O'Sensei's portrait is usually displayed above the kamiza (the head or top of the tatami mat) to show reverence and respect for O'Sensei. It is a way to say thank you for giving us this gift that is aikido. (now, what people want to do with this gift... that's a whole other discussion.)
As to why some dojo's do and do not display his portrait... I suppose that can be a touchy subject. I would venture that most reasons involve the head sensei's belief in his "affiliation" or "style", and the founder(s) of those respective categorizations.
JUST AS AN EXAMPLE: you may see in some Ki Society dojos a portrait of Koichi Tohei sensei, or sometimes no portrait of anyone at all. I suppose it a question that involves to whom aikidoka should give their loyalty and respect to. Does it show disrespect that some dojos do not display O'Sensei's portrait? I don't know if I can answer that question; it's a touchy subject.
Maybe this didn't help too much, did it?