Q. What is the significance between Jesus feeding the 4000 in one case and the 5000 in another?
A. While both events really happened, both also have highly symbolic meanings, and are aimed at different audiences.
The feeding of 5,000 was more Jewish in its nature. It happened near Passover time, there’s a veiled reference to the 23rd Psalm, and there were 12 baskets left over. The number 5000 implies the advent of the Age of Grace. It symbolized that Jesus, the Bread of Life, was sufficient to satisfy the spiritual hunger of the 12 tribes of Israel, represented by the 12 baskets. The Feeding of the 5000 is the only pre-resurrection miracle to be included in all four gospels, and you have to read all four accounts to get the full impact.
The Feeding of the 4000 is contained only in Matt. and Mark and like the 5000 includes a mass healing. It’s more for the Gentiles, four being the number of the Earth and the 7 baskets left over, combined with the healing, shows His divine ability to completely meet the needs of all the Earth.
Here’s a link to the article I wrote comparing these two events for more detail.