Bastien and Bastienne…and Beethoven?

Musical mystery, or compositional coincidence?  Wolfgang Amadeus Mozart wrote the music for his one-act opera Bastien and Bastienne in 1768, at the age of 12.  The short Overture to Bastien and Bastienne bears a remarkable resemblance to the opening theme of Beethoven’s Eroica symphony, composed between 1802 and 1804.  Although the keys are different (Mozart’s overture is in G major and Beethoven’s symphony is in E♭ major), could it be that Beethoven had Mozart’s theme in mind while he composed his 3rd symphony?  It is unlikely that Bastien and Bastienne was known to Beethoven, as that music received its first public performance in 1890.  Perhaps, just a coincidence.  Great minds think alike, it appears.

Overture to Bastien and Bastienne, Statatskapelle Dresden, Sir Colin Davis, RCA 74321-56698-2
Symphony No. 3, “Eroica”, Chicago Symphony Orchestra, Sir Georg Solti, London 430 792-2