I first encountered Wilfred Owens' "Dulce et Decorum Est" several years after I'd studied Horace's ode (III.2.13) from which Owens takes the line "dulce et decorum est pro patria mori" ("it is sweet and proper to die for your country"). What struck me was the contrast between Owens' extremely melodramatic language and the cool, controlled tones of Horace that set out out a Stoic ideal. The poem by Owens seems cinematic in its visual intensity, and seems to demand being read aloud rather than on the page.
Sassoon, by contrast, is a more subtle and elegant writer, relying more on irony that Owens, and using controlled, precise, poetic techniques rather than overwhelming the reader with gory imagery. While Owens' poem is designed to make readers feel, Sassoon makes us think. Horace and Sassoon appeal to me more than Owens, but that is really a matter of taste.
As you work on this assignment, be aware (and here I speak from over 20 years of teaching literature on the university level) that there is really no "right" answer. What your teacher is looking for is how you can relate the poem to your own feelings about war or violence, and your own personal experience. Do you like the directness of Owens? The irony of Sassoon? No one can really help you decide what you enjoy -- your tastes and responses are unique to you as an individual.