JComboBoxes have a preferred size that is larger than a JTextField.
GridBagLayout uses only preferred size, not minimum size.  So if you
really want to make the JComboBox smaller then you will have to do some
tricks.  Set the minimum size to 1,1 and reset the preferred size to
match the height of the JTextField.  I think I would just let my
JTextField get bigger to match the JComboBox but it does appear to work.

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class test extends JFrame {
    String[] array = {"one","two","three"};

    public test() {
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setLayout(new GridBagLayout());

        GridBagConstraints c = new GridBagConstraints();
        c.insets = new Insets(2,2,2,2);

        JComboBox cb = new JComboBox(array);
        JTextField tf = new JTextField("test");

        System.out.println(cb.getMinimumSize());
        System.out.println(cb.getPreferredSize());
        System.out.println(tf.getPreferredSize());

        cb.setMinimumSize(new Dimension(1,1));
        cb.setPreferredSize(new Dimension(cb.getPreferredSize().width,
         tf.getPreferredSize().height));

        add(cb,c);
        add(tf,c);

        pack();
        setVisible(true);

        System.out.println(cb.getSize());
        System.out.println(cb.getPreferredSize());
    }

    public static void main(String[] args) {
        Runnable r = new Runnable() {
            public void run() {
                new test();
            }
        };
        EventQueue.invokeLater(r);
    }
}