400 to 430 gr bullets perform much better than lighter bullets.
The 450 gr weight mentioned are not freely available in 416 caliber but rather in 404 Jeff.
A 400gr .416 caliber bullet has the exceptional SD of .330 which is part of the reason it has been so successful in Africa on DG. Therefore 400-430 gr bullets would be the best choice.
As mentioned by others above when loading the heavier for caliber bullets(more than 400gr in .416) the Rigby is the best platform for this, due to ample case capacity and the ability to keep pressures low.
Controlled expansion, forward weighted bullets are the way to go. These include Rhino solid shank, Trophy bonded bear claws, North Fork and Swift A-frame.
Woodleighs are not controlled expansion bullets.
Weights for these range from 400 gr to 430 gr bullets. Rhino made a 450 at some stage but then backed the weight off to 430 gr.
450gr bullets are the prefered weight in .404 Jeff as they have a bigger diameter than .416.
When hunting DG, especially Cape Buffalo the more bullet you have to work with the better they perform (weight retention, expansion, straight line penetration). Ideal killing speed is 2200-2400 fps.
Here is my post from the other thread regarding, which was about the 404 Jeff and why I do not like Barnes X or Woodleigh bullets for DG hunting, especially Cape Buffalo:
Here is the link to the entire thread which you may find interesting.
https://www.africahunting.com/threads/what-bullet-for-my-404-jeffery.39935/
To start with I am an old school hunter and have always been an advocate of heavy for caliber bullets irrespective of caliber used. They just perform better. They stay on course better(through brush and after hitting the buff), they penetrate better, they expand to a bigger diameter after impact as there is more bullet to do so). Typically 2.5 x diameter with the Rhino bullet.
You typically get two thoughts on this. Lighter higher velocity bullets and then slower heavy bullets at reasonable velocity(2200-2400 fps).
Firstly I would only recommend clients to use premium grade soft/controlled expansion bullets and no solids on buffalo.
I also prefer non monometal softs and also do not like the new "fragmenting" types.
Availability of bullets will obviously be an issue as all bullets are not available in all countries.
My recommendation in order of preference for bolt actions would be:
Rhino controlled expansion soft, Trophy Bonded Bear Claw, North Fork or Swift A-frame.
Bullet weights:
375 H&H-Min 300gr @ 2400 fps better 350gr @ 2300 fps or even the 380gr @ 2200 if it stabilizes and you have no pressure signs in your rifle.
416 Rigby- 400gr @ 2400, better 450gr @ 2250-2300 fps.
404 Jeff- min 400gr @ 2300, better 450gr @ 2200-2300 fps.
458-min 500gr @ 2300, better 550gr @ 2200-2300 fps. (Have to add here that I do not like the 458 Win and also not the other 458 calibers that have straight wall cases and belts). In this group I only like the 450 Rigby or the 458 Sabi.
505 Gibbs- 550-600grn @ 2300 fps.
500 JEFF- 570 grn @ 2350 fps-this is what I use for hard skin DG hunting.
Double rifles:
If your double regulates and is safe to shoot with above mentioned bullets I would go with the same. They rarely do and the best bullet to use in a double would be a Woodleigh bonded one.
The lower velocities of the big NE cartridges compliment the softer design of the Woodleigh very well and they therefore perform as designed @ these lower velocities.
Let me elaborate on why Barnes TSX would not be my first choice (for DG) hunting.
Many speak highly of the Barnes TSX and as seen here many report good results with them over a large range of calibers and species hunted. Yes they work and they work better at higher velocities on softer game. They do not work so well on hard skinned game at slower velocities.
Issues and below par performance I have seen or experienced with them are:
1. Being of monometal design they are typically longer than conventional/lead containing bullets of the same weight. This is fine if you use a rifle and caliber with a long enough magazine and action. Bullets can then be seated forward to not reduce case capacity and keep pressures down. This problem is compounded when using them in Magnum cartridges built on standard length actions. High pressures are the main cause of stuck cases/rifle jams while hunting in higher temperature areas.
2. Monometal bullets cause more friction in the barrel and also create more pressure than conventional bullets. Moly Coating helps but TSX are not coated.
3. Monometal bullets(especially copper cause more fouling in the barrel again increasing operating pressures.
4. They are spitzer shape with a slight boat tail, great for long range shooting but not great for close up work in heavy cover. Spitzer designs deflect much easier than more conventional designs. All shots taken will not always be "the perfect shot".
5. The spitzer shape is more prone to deflecting and veering off course after hitting the target.
6. The overall design is of rear weight design(the back is heavier than the front). If the bullet only partially expands(seen this on a few occasions), the rear being heavier and carrying more momentum than the front of the bullet wants to overtake the front and the bullet has no option but to tumble. This severely affects the bullet performance and straight line penetration.
7. Unreliable expansion. They often do not expand or do not expand properly. This again severely affects the performance of the bullet. If it does not expand it tends to over penetrate and exit which can lead to problems if you wound another buff behind the one being shot at.
8. I know the main animal discussed is buff but they are too soft for some applications and too hard for others. They are too hard for cats and too soft when hitting hard shoulder bones eg. shoulder on buff. This again causes either insufficient expansion(vital when hunting cats) or they loose petals when encountering hard bone which defeats the object. I need a soft to punch through, retain the petals and destroy the vitals behind the heavy bone and then settle under the skin on the opposite side.
9. A proper expanding bullet will typically expand to 2.5 x diameter and retain it's petals. The monometal expanders do not achieve this, if they expand as designed you are lucky to get 2 x expansion, most times much less.
For DG back-up you need a bullet that will perform as designed every time you need it to, the ones I have mentioned do so and the one that has been most consistent and devastating for me has been the Rhino.