Flash and teleport are forbidden (for evident reasons), all the others (including ghost) are allowed.
Basically, you can't cast anything teleporting you nor trigger an action that uses your tail (as it is used by ulti), these actions include auto-attacks and E.
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
This is the location and filename of the file that gets edited whenever I change an itemset. This is of course only as current as of today and might change with newer patches.