There are several advantages:
- The size is half of Tether (3.5 vs 7);
- Popper.js doesn't need any additional CSS in your page;
- It works even with elements not placed as direct children of body;
- It's much much faster (compare both on mobile, you'll see Tether lagging a lot!);
- It automatically detects the size of the tooltip arrow;
- Inside Popper.js you already have a way to create tooltip elements automatically, with Tether you need an additional library;
- Popper.js supports particular "flip" behaviors, you can decide that if there's not space on the left, the tooltip must move on the bottom (for example);
- The whole code is fully documented with JSDoc!
I hope this answers your question