Mozart or Chopin?

I wouldn't say that they're "aurally the same". They both contain a section with a similar rhythmic pattern – a quarter note followed by a dotted eighth and a quarter note – that gives you the "da-dah-de-da" section of the melody. It's likely that both melodies are based around music that was traditionally used in church funerals.

I think that was basically the rhythm for funeral music at the time. Its also in other pieces, that follow the same chord progression and pattern, but yet they all have a different sound.

What is known as "Funeral March" is the third movement, Marche funèbre: Lento, of Frédéric Chopin's Piano Sonata No. 2 in B-flat minor, Op. 35. Mozart didn't write a "Funeral March." His two most famous funeral pieces are his Maurerische Trauermusik (Masonic Funeral Music) in C minor, K. 477 (K. 479a) which is based on a Gregorian Chant, and his Requiem in D minor, K. 626