How could I compare Catherine Petkoff's description of a cavalry charge with that of the fugitive Swiss soldier?

The first thing you should do as you work on this assignment is think about the differences between the two characters.
Catherine Petkoff is an upperclass Bulgarian woman with no personal experience of military conflicts. As you discuss her background, you should pay particular attention to the ways the arts and patriotic enthusiasm may have colored her understanding of the events she describes. Her understanding of Sergius leading the charge and its magnificence is based on second or thirdhand evidence.
Captain Bluntschli is a Swiss mercenary. As you discuss his understanding of the charge, you should explain that he was an eyewitness and evaluating it from a purely professional perspective, in terms of its tactical effectiveness. You should also note that while Petkoff is romantic, metaphorical, and enthusiastic, the Swiss is literal, pragmatic and cynical.
Another key point you discuss is the difference between the breathless, disconnected hyperbolic language of Petkoff and the dry understatement of the soldier. Petkoff describes:

... our gallant splendid Bulgarians with their swords and eyes flashing, thundering down like an avalanche and scattering the wretched Servian dandies like chaff ...

Her language is redolent of Romantic poetry rather than of literal precision.