How to describe Elsa Schneider in Indiana Jones and the Last Crusade?

Elsa is essentially a female Belloq (the main antagonist from Raiders of the Lost Ark):

• Both have some genuine feeling for someone from the other sex, but neither lets it get in their way of working for the Nazis.
• Both have genuine interest in archeology
• Finally, both get done in by their ultimate grab for power, trying to possess a relic which could grant them power over their masters, but instead kills them.

While Barry is quite spot on with his characterization of her as a female Belloq, I'd say she was a more ambivalent character than him, and not as easily chracterizable as a bad girl.

While Belloq had some problems with the Nazis' treatment of Marion, he certainly was quite at terms with his collaboration with them, even if he wasn't sharing their ideals. Now, it may be that Elsa was just more emotional than Belloq, but, to me it seemed like she was in a much larger conflict because of her collaboration with the Nazis than he was. This is shown in her reactions at the sight of the book burning ceremony (which goes against her ideals as a discoverer and pursuer of knowledge) and the death of one of the members of the secret order in the desert and his dying words (which might also have reminded her of the fact that the grail is more than just a simple archeological relic). In fact, I don't think that she strived so much for the power of the grail, but, rather for the mere discovery of it, especially since "Elsa never really believed in the grail". In the end she was more of a pursuer of truth and knowledge rather than power, I think (which is why she might have had a bigger problem with the Nazis than Belloq had), and therefore more similar to Indiana Jones himself.

And, in line with AidanO's comment, I think especially in her similarity to Indiana she also helps to demonstrate that there are limits to what one can know and find, and that there are things more important than mankind's striving for more knowledge and relics. This is demonstrated at the end when she doesn't respect the limit of the grail not being able to move beyond the great seal and dies trying to salvage it. In fact even Indiana risks his life in the same way as she does, but unlike her he is reasonable enough to let himself get talked out of it by his father. In the end the grail itself is just a cup, not worth a single archeologist's life (and even his father has finally realized this after a life in which his son "was less important to him than people who'd been dead for 500 hundred years in another country", or a supposed ming vase for that matter ;-)). So, while Elsa somehow represents the urge of mankind for discovery and development, she also represents the problems of pure rationalism and disrespect for the things not supposed to be known and discovered (yet a moral I don't necessarily share myself), which in my opinion also fits to the slightly spiritual atmosphere of the whole movie.

And, last but not least, she also served as a more interesting love interest to Indiana due to the conflict of them being on opposing sides. The fact that she was, simply spoken (yet very simply, given the above elaborations), a bad girl and more or less a female equal to Indiana himself provided much more conflict and a more mature angle to her relationship with Indiana than if she had just been yet another damsel in distress like in the previous movies (especially compared to Willie Scott from The Temple of Doom, who was even more like a kid than Shorty was). This might be in line with the movie in my opinion being the most serious and mature of the whole franchise (yet of course still with the general lightheartedness we love Indiana Jones for).