What Twilight sees in her Soulgaze with Harry: a lonely warrior, bloodied but unbowed and treading the line between light and dark, marching alone to defend his city from the monsters who would destroy it. Bonus CMOF when the warrior faces the monsters: he laughs mockingly at them, flips them the bird, and charges headlong at them before they can do anything. Yeah, that's Harryinanutshell. While obviously non-canonic, it describes what Harry does very well.
They each have their moments. Notable ones include, but are not restricted to:
Harry using the power of the Elements of Harmony to supercharge his fire spell to kill the Nightmare. This was after actually noticing that he was possessed to begin with, and mentally caging the Nightmare first. Something that Luna, a GODDESS (or at least equivalent to a Fae Ladynote Maybe as powerful as a Fae Queen.), admits to being a little envious about.
In Chapter 6 of False Masks, Harry vaporizes a runaway cart that's about to crush him and the Cutie Mark Crusaders, leaving nothing but a crater. Even he's a little surprised by how powerful his spell was.
Harry and Rainbow Dash fighting a Hydra in False Masks 7 and defeating it with the power of poisoned candy.
Pinkie Pie cheerfully tricking the palace guards sent to guard Harry, Rainbow Dash, Applejack, Rarity, Fluttershy and Spike and the triumphant return of sleeping candy at the end of False Masks 12.
Bon Bon: You’re a man of iron and blood, stone and fire. Touched by darkness, but not overcome by it. Beaten and damaged, but unbowed. Unrelenting in word and deed, in thought and creed. You would lay siege to Tartarus itself if that’s where Twilight had been taken. And all because she’s your friend. Because you would do anything to keep her safe. Because you care.
Even if it's only temporary and Celestia is injured in the process, in chapter 18 of False Masks, the Princesses vs He Who Walks Behind. Luna drives ice and shadow spikes into its body and Celestia insta-banishes the Demon by driving her hoof through its skull. Don't mess with the Princesses of Day and Night.
He Who Walks Behind gets a few as well. His bite lays Celestia low for a while, and when the two of them have a rematch, with Harry assisting, He Who Walks Behind is winning until he's hit with the Harmony Beam. Which he proceeds to resist for several seconds, something no villain has ever done before.
Credit where credit is due: if not for the Princesses throwing spanners left and right, Novel Notion's plan would have worked.
Chapter 24 has one awesome battle that sadly takes place offscreen. On one side: Michael, Sanya, Morgan, and the Gatekeeper. On the other side: the real Obsidian the Undying and his lesser demons. How could it not be awesome?