The Tomb Raider trilogy I'm going to talk about includes the following games (released in exactly the order I have them listed):
Tomb Raider: Legend
Tomb Raider: Anniversary
Tomb Raider: Underworld
There are a few things that appear to be worth mentioning.
First, even though all the games in the trilogy were built on the same game engine, namely Crystal Dynamics engine, they use the different versions of that software. It looks like the versions of the engine are not actually mentioned to the public and a whole bunch of games use the same engine title. Deus Ex: Human Revolution and the 2012 Tomb Raider game both are powered by the same tech. Nonetheless, Legend and Anniversary appear to be sharing the same version of the Crystal engine (even if the engine was updated for Anniversary, the changes were minor). Underworld, on the other hand, is a whole new breed of beast. The visuals and, most importantly, performance are completely different from what is seen in the prior two games.
to be continued...