I would without a doubt recommend the 500 Jeff.
In 458 Caliber I would only consider the 450 Rigby, I would stay away from a 458 Win. I would much rather use the 404 Jeff that you have or 416 Rigby instead of a 458 Win.
The 458 LOTT achieves what the 458 Win was supposed to achieve in the first place, only gripe I have with it is the straight walled case and belt. With the 500 Jeff you get superior performance with very similar recoil.
Below some of my thoughts regarding the 500 Jeff and DG back-up rifles:
Before the 460 Weatherby arrived on the seen it was the most powerful hunting cartridge.
It is devastatingly effective on DG even in the most dangerous circumstances.
It does not have a straight walled case(a good thing on a DG back-up rifle).
It does not have a belt(another good thing on a DG back-up rifle).
It has a rolling recoil rather than a sharp recoil which can lead to flinching and slow recovery times for the second shot if needed.
In the right action you can have one in the chamber and 3 in the mag(not that you would ever need them if the first shot is placed correctly).
The 500 Jeffery beats the significantly larger capacity .505 Gibbs in velocity and energy, while offering a broader selection of bullets for handloaders. This is achieved by loading the .500 Jeffery to a higher maximum average pressure. The 500 Jeffery operates in the 46,000 PSI range, the 505 Gibbs at 39,000 PSI. To put this in perspective, the even smaller .500 A-Square out performs both of these larger cartridges by upping its pressure to 64,000 PSI.
Both the 505 Gibbs and the 500 A-square have much more felt recoil than the 500 Jeff.
Below ballistic comparisons speak for themselves.
Ballistic performance-500 Jeff
Case capacity 158 gr H2O (10.2 cm3)
Max pressure 46,000 PSI
Bullet mass/type Velocity Energy
570 gr (37 g) Soft Nose 2,200 ft/s (670 m/s) 6,127 ft·lbf (8,307 J)
570 gr (37 g) Barnes TSX 2,507 ft/s (764 m/s) 7,957 ft·lbf (10,788 J)
535 gr (35 g) SP 2,549 ft/s (777 m/s) 7,721 ft·lbf (10,468 J)
600 gr (39 g) PP 2,468 ft/s (752 m/s) 8,117 ft·lbf (11,005 J)
465 gr (30 g) Lehigh Solid 2,551 ft/s (778 m/s) 6,721 ft·lbf (9,112 J)
Ballistic performance-505 Gibbs
Maximum pressure 39,160 psi (270.0 MPa)
Case capacity 178 gr H2O (11.5 cm3)
Bullet mass/type Velocity Energy
600 gr (39 g) Protected Point 2,100 ft/s (640 m/s) 5,877 ft·lbf (7,968 J)
600 gr (39 g) FMJ 2,100 ft/s (640 m/s) 5,877 ft·lbf (7,968 J)
525 gr (34 g) Welded Core SP 2,300 ft/s (700 m/s) 6,180 ft·lbf (8,380 J)
Ballistic performance-458 Win
Maximum pressure (C.I.P.) 62,000 psi (4,300 bar)
Bullet mass/type Velocity Energy
300 gr (19 g) HP 2,606 ft/s (794 m/s) 4,525 ft·lbf (6,135 J)
350 gr (23 g) RN 2,557 ft/s (779 m/s) 5,083 ft·lbf (6,892 J)
400 gr (26 g) FN 2,468 ft/s (752 m/s) 5,411 ft·lbf (7,336 J)
500 gr (32 g) RN 2,192 ft/s (668 m/s) 5,336 ft·lbf (7,235 J)
Ballistic performance-404 Jeff
Maximum pressure (C.I.P.) 52,938 psi (364.99 MPa)
Bullet mass/type Velocity Energy
400 gr (26 g) RN 2,125 ft/s (648 m/s) 4,020 ft·lbf (5,450 J)
400 gr (26 g) DGX 2,300 ft/s (700 m/s) 4,698 ft·lbf (6,370 J)
450 gr (29 g) FMJ 2,150 ft/s (660 m/s) 4,620 ft·lbf (6,260 J)
For me 500 Jeff all the way!