I never played Omega but that reminds me quite a bit of an old PS1 game called Carnage Heart that I played alot back in the day.
You designed giant robots, bodytypes, guns missiles, arms, engines, cooling, secondary weapons, whole works. You had two leg walkers, tank types, spider types, and if you really dumped alotta money into a company you got flying types.
And there were a number of large weapons manufacturers companies that you invested money into different design blueprints as a way to research. Most of those designs like a design for a laser weapon everybody would have their own variant of, but even those weapons seemed unique, with one companies lasers having a really high output or a low cost and high efficency, they even had brand names to give them a little more detail. But the companies usually had specialisations too, one company making very good CPUs or engines while another company makes high tech mech bodytypes.
But the game's big thing was it's AI. You made it from almost scratch. You had a number of 'chips' that you would place on the CPU in a flowchart fasion. Each chip was one command, such as "If projectile 0 degrees forward in 180 degree cone within 50 meters" and "Jump left" "Duck" "move forward" "fire primary 3 times". And all the numeric values could be changed on the chip. For example the check projectile one could be set to look in a narrower cone at 90 degrees for 200 meters if you wanted. The system was rather powerful.
And then you would mass produce the things into squads of 3 in your factories in a big turn based strategy game. And when opposing forces met they would go into a combat screen where they would duke it out using the AI you made. There was a cheat code that allowed you to directly control bots too, and the cheat code didn't really make the game any easier. But you were meant to let the AI do all the work.
http://www.youtube.com/watch?v=f8Vk7u2Niu0 <- Youtube vid of a versus fight between 2 player made designs. You can see in the large grid in the top left a representation of the AI and how it's executing things, each little block is a command. It dosn't show you the exact commands but you see how it's structured.
EDIT: I was unaware they made a PSP port of this, must not be as obscure as I thought.