Why isn’t Jesus’ model of fasting 40 days without eating anything followed, but the one “given” by the church? Which way of fasting is more important?
There is no commandment given by Jesus in the New Testament that would require all the Christians to fast 40 days as Jesus did in the desert, when He was tempted by the devil, as it is written:
Then Jesus was led up by the Spirit into the wilderness to be temped by the devil. And after He had fasted forty days and forty nights, He then became hungry.(The Gospel of Matthew 4:1-2)(NASB)
The churches decide by common accord over one fast or another for a specific purpose. If you are part of a local church, and if you share in the needs, events and activities of the church, it is right and expected from you to keep the fast announced by the church. But this is a personal choice, and nobody can force you to do it.
The answer to the second questions you can find in the article entitled “Which is the most important fast?”