I have had Poicephalus parrots for a long time and I would never put two different Poicephalus parrots together. The less aggressive one will not be able to escape if there is a fight and injuries will occur.
You even have to be careful when they are a mate bonded pair of the same species. In the wild, Poicephalus parrots do not always mate for life, and it is quite common for many of them to switch mates. The Ruppell Poicephalus was reported by Ruppell, to switch mates after each breeding season. Some breeders find that their breeding Pois just don't get along one day and they do attack each other, so Poi breeders watch closely.
Poicephalus parrots of different species can learn to get along with each other usually, over time, but they pick how close they will be and what they allow the other to do and they need space for that to happen. In a cage together they cant have space
I had a Senegal who never really liked any other parrots of any kind, but learned to just keep a distance from them. I also have a Red Belly who has formed relationships with other Pois, and who even formed a relationship with a budgie and she never attacked the smaller parrot.
I currently have two Pois. My 18 year old Red Belly female gets along fine with my young year old male Meyers. She preens him, and she lets him feed her. She will flock together with him, but she needs more solitary time than him and she will chase him away if he is being too clingy. They get along fine all day, outside their cages, and he never stays mad when he is chased away. He is a good natured guy. If they were in the same cage, My Red Belly would damage him badly and maybe even kill him.
Senegals can be very aggressive, and would most likely be the one to go after the brown head, but some brown heads can be aggressive. They may get along fine outside their cages together. but, I would never put two Pois of different species in the same cage, it is a disaster waiting to happen in my opinion.
Below is the opinion of Jean Pattison, an author of books about Parrots and Poicephalus.
"I would like to mention that many people think parrots mate for life, but this is not the case. It has been shown that wild parrots switch mates after years together. In captivity, birds that have been breeding and raising chicks for years might all of a sudden turn on each other, and one is killed. Knowing the signs of mate aggression ahead of time has prevented many deaths with breeding pairs. In these cases, they are separated and placed with new mates to live many years together. In knowing this, it may not be wise not to purchase a "friend” for your Poicephalus. If an owner wants another Poicephalus, then by all means they should get one, but they should not think it will be a buddy or mate for the one they already have. The small Poicephalus are quite happy being the center of attention."....Jean Pattison.