Katarina's ultimate, Death Lotus is a channeled ability (as you may notice in the cast bar that appears and counts down). Like any other channeled ability, taking any other action, such as using an item like Zhonya's Hourglass, will interrupt the channel.
Other Champions, for instance, Fiddlesticks, Kennen, or Morganna, don't need to channel to maintain their ultimate, meaning Zhonya's can be used to safely shield them for its duration.
The question depends on what you want your role to be... or, if you're getting stomped in lane, what role you can be ;-)
Death obviously grants you a ton more damage by giving you the DoT (Damage over Time) effect. In fact (from League Of Legends wikia):
Magic Damage: 70 / 115 / 160 / 205 / 250 (+0.7 per ability power)
Total Damage With Augment: 91 / 150 / 208 / 267 / 325 (+0.91 per ability power)
That's... a big deal. Especially for an AoE ability.
However, it does leave Gravity Field a little weak because of how vulnerable you have to make yourself to cast it into a teamfight. Moreover, Augment Gravity doesn't just make Gravity Field stronger:
Gravity Field has an additional 30% cast range. The item now grants
him +3 ability power per level, +200 mana, +10% cooldown reduction and
+5 mana regeneration per 5 seconds
Now that we know the benefits... Which one is better?
If your team is relying on you to dish out a ton of magic damage, for instance if you have a tankier team or an AD-heavy team (forcing the opponents to build armor to cope), then you almost have to get Augment Death. Viktor's entire damage kit was balanced around that idea. If you don't, you'll be hamstringing your role.
However, if your team lacks a lot of CC; has an initiate that brings the enemy team into a tight formation (Shen taunts, Orianna ults (because you have two AP? I don't know); your team has a lot of gap-closers (Irelia, Xin Zhao, Jarvan, etc.); or if you're just behind and need to be helpful in a different way, you want to get Augment Gravity.
TL;DR: Augment Death lets you crank out the damage, but your team utility will be low. If your team needs the additional utility, or you're too far behind to do meaningful damage, Augment Gravity.
Best Answer
You're right. The best way to use Zhonya's Hourglass is by using it in a teamfight. Lightning Rush in, try to hit as many targets as you can, then activate Electrical Surge, then Slicing Maelstrom. Here is the description for Kennen's ultimate, along with the description for Zhonya's hourglass, from the League of Legends wikia page.
Add this to your two marks of the storm on each opponent with your E-W combo, along with any Marks of the Storm added from your ultimate before using Zhonya's hourglass. You can potentially stun all opponents.
Since Kennen's ult is very powerful due to its utility, enemies will try to focus you down to avoid stuns. That's when you want to Zhonya's. When it's active, you will continue to stun enemies.