It's pretty much impossible to compare them. That's like saying "Let's take this sculpture and compare it to this oil painting and see who's the better artist." You can judge them on their musicianship and they ability to express themselves through their art but their style of music are completely separate from each other. It might not be too far-fetched to say their styles are almost like different mediums.
My personal favorite from the two would be Chopin however I'm a great fan of Tchaikovsky himself. He had a very interesting life.