There are substantial numbers of people who feel the .404 Jeffery is the better cartridge. I’ll take a Jeffery any day over a 416. Remington
Likewise, there are also many people who think the 257 Roberts is better than the 6.5 Creedmoor. And they're wrong as well! The 416 Remington and 404 Jeffery have cases and bores of similar size, and therefore these two cartridges have the same performance. The 416 is the clear practical choice due to lack of support for the 404's uncommon .423 bore.
The 404 does only one thing better: it's got a cooler name!