Battlefield Victory or Martyrdom! Which one is better?

Jabir narrates: The Messenger of Allah (P.B.U.H) was asked about the best jihad. He said: “The best jihad is the one in which your horse is slain and your blood is spilled” [Reported in Ibn Habbaan, Ahmad and Ibn Abu Shaybah]

Amr bin Absah narrates: A man said O Messenger of Allah (P.B.U.H) what is Islam? He said, “Islam is the submission of your heart, and that the Muslims are safe from your tongue and your hands” He said: “What is the best of Islam?” The Messenger of Allah (P.B.U.H) said, “Iman (Faith)”He said what is faith? The Messenger of Allah replied, “To believe in Allah, His angels, His books, His Messengers, and the resurrection after death” He said, “What is the best of Iman?” The Messenger of Allah (P.B.U.H) said, “Hijrah” He said what is hijrah? The Messenger of Allah (P.B.U.H) said, “To leave sins behind” He said, “What is the best of hijrah?” The Messenger of Allah (P.B.U.H) said, “Jihad” He said what is the best of jihad? The Messenger of Allah said, “the one whose horse is killed and his blood is spilled” [Reported in Ahmad, al Tabarani and al Bayhaqi]

These hadiths are a clear refutation of the claim that the one who wins is better than the one who is killed.

Abdullah bin Ubaidillah bin Umair said: Amr bin al Aas was circling the Kaabah when he passed by a circle of men from Quraish sitting down. When they saw him they asked each other who was better:
Amr bin al Aas or his brother Hisham? When Amr finished his tawaf he walked up to them and said: “I heard you say something about me, what was it?” They said: “We were wondering who is better you or your brother Hisham” Amr bin al Aas said: “I will tell you about that. I was with my brother Hisham at Yarmuk and we spent our night praying that Allah blesses us with martyrdom. The next day my brother got it but I didn’t. So you can then see that he was better than me” [Reported by Ibn al Mubarak]

This is a clear-cut statement from Amr that the one who is killed is better than the one who is not.