"Although Perry spoke very highly of Elliot in his official report and Congress decorated him, rumors of Elliot's animosity against his commander and observations from both British and United States experts that Elliot had not backed Perry's boldness as he should created a simmering controversy. Various accusations and cross accusations in the press, including a defense by James Fenimore Cooper, resulted in Elliot challenging Perry to a duel and then facing a court-martial, a situation that the Cabinet desperately wished to avoid." [Source]
Indiana University has included a copy of Elliott's vindication as well as a brief summary of the feud between Perry and Elliot(t) :
THE PERRY-ELLIOTT CONTROVERSY
Alexander Murray. Opinion of the Court of Inquiry on the conduct of Jesse Duncan Elliott in the Battle of Lake Erie. 1815. (copy) A handwritten copy of the court opinion clearing Jesse Elliott of any wrong-doing in the Battle of Lake Erie.
This site has a cast copy of Captain Jesse Elliott's Tribute Medal to James Fenimore
Cooper (the Fenimore Art Museum also has a copy of the medal online).