Symbolism, Imagery, Allegory
Old Rossum and Young Rossum aren't characters in the play as much as stand-ins for different approaches to modernity and faith. You could call them Old Atheism and Young Agnosticism if you wanted (they probably wouldn't answer if you called them that, but you still could).
Old Rossum is a big old materialist atheist—he doesn't think there's a God, and he doesn't want you to think there's a God either. Everything is just material—that is, he only believes in what he can see and build. There's no spiritual whatsit out there, just the bodies and materials that you can grab onto and yank. Rossum thinks robots are awesome because he can use them to prove that atheism is the truth:
"He wanted to somehow scientifically dethrone God. He was a frightful materialist and did everything on that account. For him the question was just to prove that God is unnecessary." (prologue.76)
Young Rossum, however, is a different kettle of robotic protoplasm. He doesn't care if God exists or not; he just wants to make better faster, more efficient… um, efficiencies. Young Rossum is an engineer, and when he sees his dad trying to painstakingly make a human being, he snorts and then snorts some more:
"This is nonsense! Ten years to produce a human being?! If you can't do it faster than nature then what's the point?" (prologue.82)
For Young Rossum, God doesn't matter; making goods and producing money, or making money and producing goods, is the important bit.
So Old Rossum is a vision of modernity which deliberately wants to put humans in the place of God by demonstrating that materialism is true. Young Rossum doesn't care about God or materialism at all, just about materials. They quarrel with each other and sneer at each other and even curse each other. But in a lot of ways they're allied. They both are focused on this world; they both put humans in the place of God—either deliberately, like Old Rossum, or by default, like Young Rossum, who has man create and create without thinking about God. Nana of course would think both were blasphemers since, "All inventions are against the will of God. It's nothing short of blasphemy to want to take over for Him and improve the world" (1.328).
In different ways and for different reasons, both Old and Young Rossums are trying to take over for God. And they both succeed, sort of, though at the cost of exterminating the human race all together. You can get rid of God to put humans in His place, the Rossums show, but only if you get rid of humans too.