Another 2 cents.
S American cichlids seem to me (in general), to have much less aggressive tendencies than Centrals.
Maybe its because S America has a much more diverse population of cichlids in the same habitat, and this allows them to be much more tolerant of each other.
Even with that natural diversity, I prefer to house different genus together.
I am able to keep the S American, Guianacara sp, Crenicichla belly crawler and xCichlasoma ornatum in the same 6ft tank together with a fair amount of tolerance, I believe, because each is very dissimilar to the other.

In Central America, you very seldom see 2 of any one genus in the same area (other than some Thorichthys).
It may be simply one of my idiosyncrasies, so beside not mixing continents, I also think keeping 2 Central Amer cichlid species of the same genus together in the same tank tends to cause trouble.
To me keeping 2 Cryptoheros, or 2 Vieja together in a tank under 300 gallons is a recipe for aggression, because in nature they would be direct competitors for food and breeding sites/territories.
Whereas say, a Chuco intermeda may tolerate xCichlasoma bocourti because they
seem to have an instinctual sense they are not going for the same things.
Their different body shape, and mouth formation both indicate different preferences, and because of this I have had success (at least temporarily) keeping them together in the confines of the relatively small space of a 6ft tank.

By simple observation of mouth and body shape, it seems that putting 2 Parachromis species together, or with a similar genus, ie Nandopsis would be tempting battle.

I try to always keep any species of the same genus apart, be they Cryptoheros, or Tomocichla.