Haven't heard enough of Chopin beyond his "Funeral March" to draw an opinion on him, but Tchaikovsky holds a special place in my heart, if only because of BioShock (there's a sequence involving blowing enemies away to "Waltz of the Flowers" ).
Granted, I hated The Nutcracker when I saw it, but a few of the songs are favorites of mine. Not to mention you can't go wrong with the "1812 Overture" with black powder cannons in the background- I joke around that if I ever join an orchestra, my instrument will be the howitzer.
Chopin is like God to me. To create "technical pieces" and compose them in a way that they'd stand out as songs in their own right. Chopin's a genius with incorporating his own soul into his melodies. He didn't create the nocturne manner of compositions, but he revolutionized it. He pioneered the Legato/Rubato style of playing. His Andante Spianato & Grand Polonaise Brilliante, I'm performing soon. I could listen to this piece for days. The 2nd movement to his 1st Sonata, Op $ is so soothing. Around 1:43, I get the chills when he deploys poly-rhythm .
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Though, at the end of the day, I could never compare Chopin with Tchaikovsky. Their styles and reasons for composing are too different. Tchaikovsky composed for Orchestra's, whereas Chopin's main focus was solo piano.