There is nothing wrong with the .404 Jeffrey, quite the contrary. But if it was the do all to end all of 40 something calibers what are we doing with all those others?

The .404 Jeffrey and .400 H&H are different cartridges. Period. The world can exist with both and deciding which one a shooter wants in his rifle is a matter of personal choice. We have seen the endless debates between 7mm Mag, .270, and .30-06, and, a long time ago, the .338 Win Mag and .358 Norma. Shall we debate the .338-06 out of existence because the .330 caliber .318 W-R has been around for over a century? Are we to engage in such a debate now?

The cartridges are simply different:

The H&H is a .410 caliber but the Jeffrey is a .423 caliber.
The H&H is better suited to a "standard" magnum action while the Jeffery is better suited to a "true" magnum action. Yes, both can be built on both actions but each is better sized for one action over the other.
The x-sectional area of the .400 H&H bullet is .13 in² while the x-sectional area of the Jeffrey bullet is .14 in². That accounts for the slightly higher sectional density and ballistic advantage the H&H round has over the Jeffery. For example, the SD of a 400 grain bullet is .340 for the H&H vs .319 for the Jeffery.
The Jeffery cartridge is slightly bigger (113gr H20 vs 104 grains H2O) but the H&H is slightly more powerful because the H&H is loaded to higher pressures (that nasty belted case!).

The list is not complete. But even if it were it doesn't mean one is any better than the other. It only serves to illustrate that they are different.