They are different products and very difficult to say which is better. I have both and use them for different reasons.
Airtel Internet TV is Android TV box with catch up TV.
You can record, pause and replay programmes. This is one biggest feature in favour of Airtel Internet TV. Earlier they had costly packs for Airtel Internet TV which will not the case now after TRAI new rule.
Use USB for media files.
Inbuilt chrome cast.
One box, one remote and one HDMI port require.
Still evolving and might add more features.
For Amazon Fire TV
More apps are available.
Little more smooth navigation and stable. But can say that diffrance is very little.