Why did the Black Captain switch rides?

[luthien-elvenprincess]

Opinions please...based on Tolkein fact, of course!

Upon leaving Minas Morgul and at the gate of Minas Tirith, the Lord of the Nazgul is riding upon a black horse. But, he switches to the winged beast after meeting Gandalf on Shadowfax at the gate of Minas Tirith. Why?

Because the winged beast was faster? Because Shadowfax was a greater horse than his, even though his withstood the onslaught at the Ford of Rivendell?

The Nazgul Black Captain would have had to leave the gate, switch beasts, gotten to the battle field to kill Theoden, and then be defeated by Merry and Eowyn in a matter of probably 3 hours. Gandalf and company heard the dying cry of the Black Captain while arriving at the Houses of Healing with Faramir. I figured 3 hours because Gandalf and Pippen first arrived at Minas Tirith at sunrise (6 AM) and was up in the Citidal prior to 8 AM. I suppose that Gandalf was hurrying even faster up the levels of minas Tirith to help Faramir than when he first arrived. Another hour to rescue Faramir, deal with Deneathor, and then carry Faramir to the Houses of Healing make up the 3 hours I figured between the Black Captain leaving the gate and dying.
AGain, my question: why did the Black Captain switch beasts?