Thief 2 switches out the factions, but otherwise things are exactly the same, but the level design of the two games reflects this. Thief (Gold) focused on the Pagans as they rose from the shadows and tried to claim the world for themselves, and only by the intervention of the Keepers and their agent 'in the field' were their plans foiled.
Now, each of the three games focuses upon one faction, leaving the other two lurking in the background. The Pagans are not exactly a polar opposite to the Hammerites, but they're a good contrast: The supernatural, the unexplained, the emotional, the absence of logic, etc. Each faction has familiar themes and tropes for them, such as the Hammerites representing organized religion, fundamentalism, the application of the logical in the pursuit of knowledge at the cost of the emotional, and so on. The Thief series is a trilogy of games exploring three factions and how they affect The City: The Pagans, the Hammerites and the Keepers.
I'm with JarlFrank, though I'd like to add one thing to silence people like HansDampf here above:
