While they have similar length[1][2], roughly 6500-7000 km, the discharge from the Amazon is roughly two orders of magnitude greater, 4200 m^3/s vs 209000 m^3/s average.

There's also a lot more Amazon river to hold water.

[1]: https://en.wikipedia.org/wiki/Nile

[2]: https://en.wikipedia.org/wiki/Amazon_River

Means the volume of water and flaw rate, in the Nile is much less than the Amazon river.