As the title asks, why did Harry's wand not reveal its last spells during Priori Incantatem with Voldemort in Goblet of Fire? Voldemort's wand revealed Wormtail's severed hand, Cedric Diggory, Frank Bryce, James and Lily Potter, Bertha Jorkins, and screams of pain (Cruciatus, perhaps? As Avada Kedavra isn't painful in and of itself) -- why didn't Harry's wand do the same?
Harry was able to win the 'battle' between the wands. The pulsing bead that was on the beam that connected Harry's and Voldemort's wands connected with Voldemort's wand due to Harry willing it away from him with his entire being. Priori Incantatem occurred with Voldemort's wand directly after the light bead connected with his wand so we can infer that the bead hitting his wand is what caused Voldemort's wand to start regurgitating the previous spells.
The light bead didn't connect with Harry's so there was no reason for Harry's wand to start spitting out the previous spells it had been used for.
From "The Goblet of Fire":
"So what happens when a wand meets its brother?" said Sirius.
"They will not work properly against each other," said Dumbledore. "If, however, the owners of the wands force the wands to do battle…a very rare effect will take place. One of the wands will force the other to regurgitate spells it has performed - in reverse.
And, from Deathly Hallow's scene at King's Cross:
Dumbledore: He was more afraid than you were that night, Harry. You had accepted, even embraced, the possibility of death, something Lord Voldemort has never been able to do. Your courage won, your wand overpowered his.