I've been playing a lot of Zenyatta recently and I consistently get gold healing even with Mercy/Lucios alongside me on my team. He feels intuitively weaker due to the mechanic but I think he's the best offense healer; better than Lucio.

• Orb of Destruction. The orbs don't move very fast, but they're perfectly accurate, pack a punch (45 damage) and you have a lot of them to expend before reloading; almost 7 seconds non-stop firing. This lets you keep a strong presence from the back lines, where Zen belongs. You can also act as a faux-sniper or countersniper when necessary. Personally I don't make much use of his alt-fire but it has been useful for shredding beefier tanks like Roadhog or Reinhardt if they get close and make them think twice about engaging you so far removed from their team.
• Orb of Harmony. Now it might seem weaker than the other healers' heals but it's still a solid 30hp/second (Mercy's beam is 50 and Lucio's aura is 12.5). More importantly, it will stay on your heal target indefinitely as long as they're within your line of sight. This means that if you drop it on a tank like Roadhog and stick in the back lines, you can boost your team's sustain massively. It's very useful for topping up teammates who are only down a little as it's significantly faster than Lucio's aura and requires less effort than Mercy's beam. Just drop it on them, keep doing what you were doing, then reassign it after a few seconds.
• Orb of Discord. This is what makes Zen in my mind. 50% bonus damage to whoever it's on. The possibilities are pretty much endless. It cripples tanks. Makes healers vulnerable. Fucks over snipers. Anything. Drop it on an opponent in close-range and you even out the playing field significantly.
• Transcendence. It's a bit of a weak ult, but does prove he's not just a healer on the side. I find it most useful to negate enemy ults. Reaper ult? Fuck that 100 hp/s heal for everyone. Pharah ult? Fuck that 100 hp/s heal for everyone. Graviton Surge? Fuck that 100 hp/s heal for everyone. And so on. It also charges very fast if you're dishing out both damage and heals in respectable amounts.

TL;DR - Zenyatta is a long-range glass cannon. He stays in the back lines and supports his team with heals, and debuffs for the enemy. He can deal a lot of damage if you use his orbs right. His ult is useful for countering enemy ults and pushes.