In season 2 Molari and G'Kar both state that the first contact between Centauri and Narn was 150 years ago. The first contact between Earth and Centauri was 100 years ago. Yet the outcome of both was quite different, even though Earth was still quite technologically primitive compared to the Centauri. Why didn't the Centauri enslave humans and exploit the Earth like they did Narn?
UPDATE: JMS spoke to this specific issue in a webchat in 1994, basically confirming everything I put in my original answer :-)
What was the Centauri relationship to Earth?
The Centauri never really got around to us. They've been in a decline for a long time; the Narn occupation was one of the last of their imperialist rampages. Now they're pulling back further and further. And also as re: Earth...space is big. 100 years ago, we weren't putting out any radio or television or microwave transmissions; they can't check EVERY planet. We got overlooked for a long time by lots of different groups.
While we were in an agrarian state, and an early industrial state, we a) were of very little use, b) had little to offer, and c) came at a time when the Centauri were starting to fall back into isolationism just a bit. The Narn had the misfortune to be strategically well located, had many resources the Centauri wanted, and provided other advantages. One doesn't just conquer worlds helter-skelter; it takes time, money, effort and some blood to conquer worlds. You only choose those which offer you enough to make the process worthwhile. That simple.
It's stated (ad nauseum) that the Centauri Republic is in terminal decline. There was some sort of incident (never described but repeatedly hinted at) that caused the Centauri to embark on a radical change of policy a couple of hundred years before, ending the occupation of Narn worlds, drawing back from their own colony worlds and attempting to seek out potential allies among the outlying areas of space outside their immediate control.
Why did they invade Narn?
Narn is described as a peaceful largely agrarian society. The warlike (and highly sophisticated) Centauri seem to view the Narn as little better than animals; uncivilised and basically living in their own filth if left to their own devices.
The Narn worlds were directly adjacent to Centauri space. Without much by way of defensive capacity, they were an easy and inviting target to an Empire seeking to reassert its dominance.
Why didn't they invade Earth?
After a hundred years of bloody occupation of Narn (and a further hundred years of post-colonial reprisals), the Centauri seem to have little appetite for another bitter conflict.
Invading Narn proved utterly counterproductive. Not only did the Centauri not halt their decline (described by JMS as "like the Fall of the British Empire") but they pushed the Narn from an agrarian society into a highly industrialised society in the blink of an eye.
The Centauri wanted allies, even going so far as to claim that Earth was a lost colony of the Centauri Republic. Evidently they were found out quite rapidly but it can be assumed that they were hoping to gain a key regional supporter, one with billions of potential workers and a pre-existing industrial base.
Earth was potentially too hard a target. It's a long way from Centauri Prime and a prolonged occupation could be prohibitively expensive.
Behind the scenes:
- The elephant in the room is that everything that happens, happens because the Vorlons (with their grasp of time travel) have already seen it in advance. Earth was never in danger of being invaded because the Vorlons couldn't allow that to happen without endangering themselves. Quite what pressure they brought to bear isn't known, but I think we can be reasonably sure that they were pulling the strings.