Good scenery and alternating of events (Kings Row, the Council)
I noticed :
* "he was in a Council uniform" and "they were megalomaniacal conquerors"
* "A group of Skulls lurked" and "the death-obsessed thugs"
You name Council and Skulls then comes a short description of what they are.
However :
* "Hellions pushed around a woman" has no more info on what Hellions are. Even if the name and the action you describe suggest another gang (like the Skulls)
* "Clockwork ripped pieces of scaffold" might need another hint about their nature different from all other groups you mention.
Council members are conquerors, Skulls and Hellions are gangs but Clockwork ?
From a CoH gamer perspective, there is no need for more, we probably all know what are Clockworks. From an outsider perspective, the word "Clockwork" is suggesting some sort of machinery but nothing more.
Still, it also depends if you plan to develop on this later, with a future text. Or if you intend to write for a CoH audience (who will identify most of the names, places, just by mention) or not.
Yet, some elements might be left in the background until explained.
Pretty much like the mention of the Templar armour. We have some physical details about the main character (she is a woman, has dark red hair, deep blue eyes) but the armour isn't described at all. It is cumbersome, what colours, unique, high tech, etc ? (we can suppose the later from the general tone).
The armour can be a plot element, to be developped later, paralleling the development of the character. It depends a lot if/how you plan to write more on the character.
Good points, frankly. 
It was written as a short piece for CoH/CoV players that already knew the basic terminology; I should really describe the armour though...thank you for the input.
Susanne sat on the edge of the building, watching the King's Row traffic roll by below her, her feet dangling over the edge. She was still clad in her Templar armour, though her helmet sat to one side of her, her trusty Multiple Weapon System on the other side. Dark red hair was disturbed by the faint breeze, carrying the stench of the city; her eyes, a deep blue shade, were dilated and distracted. She was deep in thought, and it was obvious.
She'd almost had the crate open; the Neural Scrambler was almost in her grasp; and then she'd been surprised. He'd walked around the corner, and although he was in a Council uniform, and although he was in the middle of a war zone, she couldn't help but notice the look of fear and panic in his eyes.
He wasn't another fighter. He was a lab technician, a statistical analyst; she saw a kindred spirit in him. Once, she'd been a lab technician, too - before the Templar program, before her brothers and her father had teamed up with her to craft the armour, before her father had stolen the prototype and gone rogue.
He was in a Council uniform, but he wasn't a soldier. He wasn't one of the Penumbra rifle-monkies that lined up to knock her down. He was an academic.
Down below, horns honked. A group of Skulls lurked in a nearby alleyway, spraycans painting a dark tattoo against the brick-face skin of the apartment building that cast its shadow over them.
It was easy to think in terms of black and white, in Paragon City. When the Hellions pushed around a woman and took her purse, there was no room for discrepancy. They had to be stopped. When the Clockwork ripped pieces of scaffold and chunks of steel out of the city's structures, they were building something that would undoubtedly be trouble for the citizens, and they had to be stopped.
The Council, no doubt, had to be checked; they were megalomaniacal conquerors who had big plans for everywhere on earth. It was easy to know that they were the "bad guys", as much as she was a "good guy".
The lab tech had reached for his pistol.
She closed her eyes as she saw it in slow motion. The Templar helmet and visual gear had given her a pixel-accurate ultra-high-definition image of the man's face, the sweat droplet formed on his temple, the gleam of light on his goggles, the glint of the diamond set in his wedding ring.
Her reactions in the suit were too fast. She hadn't thought. He had the pistol halfway out of its holster when she pulled the trigger, and the rifle kicked in her armoured hand.
She was a scientist. She was a creator, a researcher, an inventor; yet she couldn't remember anything she'd created since XT-01 was finished, and she'd taken to the streets in it. All she'd done was destroy and kill, and it had taken her this long to realise - not everyone in her sights had been a murderer or a mugger.
Her eyes opened.
Was that really her goal? To tear apart the enemy, no matter what? The integrated Multiple Weapon System had recently had a beanbag launcher fitted alongside the grenade tube; could she turn to it and rely on it as readily as she deployed the shotgun, the assault rifle?
Down below, three of the Skulls slipped away from the shadows, starting to follow a girl on her way home from work. Susanne didn't need the goggles to pick out the gleams of greed and darker things in the eyes of the death-obsessed thugs.
The helmet slid into place and she gathered up her Multiple Weapon System.
It was always easier, she mused, when she had a target; with nothing to fire at, she would see the blood spatter over the gold wedding ring over and over again.
She slipped off the side of the building, crosshairs picking out the Skulls as she loaded an M30 grenade into the tube.