Almost everything has been said, but the original question has, so far, not been answered...
Here it is:
There is no discernible difference in the field between the .470 NE and .500 NE. Sure, technically the .500 hits a tad harder, on both ends, but not enough that anyone will see a difference under actual hunting conditions. Buying a .470 or .500 is more, in my opinion, an issue of likes/dislikes, ammo availability (.470 is more common), and buying opportunity (the right .500 at the right price is the right choice).
Regarding the hunt:
Whether you first hunt dangerous game (DG) with a double, or a turn bolt action, or a single shot, or a straight pull, etc. the key word has already been stated: PRACTICE. I would add: practice as you will hunt. Cycle all the rounds from a fully loaded magazine; fire both barrels of a double; reload while keeping your eyes on the target; etc.
And of course, test & debug thoroughly your DG rifle. There is no such thing as an Africa-ready DG rifle out of the box - regardless of the name on the barrel - if only in as much as the best rifle is useless to you until its particularities have become second nature to you.
Double or bolt action? In view of the above, I would have a more nuanced perspective than others. My take would be that it is about as dangerous to go DG hunting with a bolt action you have not practiced with, as it is with a double you have not practiced with. Both are unwise. Where I see the most notable difference - assuming in either case that the proper proficiency has been achieved through appropriate practice - is indeed, as indicated by
Red Leg, in the fact that a scoped .375 or .416 will objectively give you more opportunities. One would say that they will not necessarily make the
hunt easier, but they will objectively make
taking the shot a lot easier, and from a longer distance. This certainly improves your chances, but this is also exactly the reason why I do not want a scoped .375 or .416 on herbivore DG, even though I own both, as well as a .458, and I will choose to hunt buff, hippo, elephant closer and harder with an open sights double. Cats are different and I reckon a scoped .416 Rigby as the quintessential lion rifle. We each pursue our own dreams...
This being said, I agree again with
Red Leg: hippo with a double has to be a terrestrial hunt. My additional thought would be that hippo on terra firma is often indeed a hard hunt if in dense bush, and it can be quite an exciting one at that; while shooting a hippo in the water is often just that: shooting. So, I would vote for hippo with a double, assuming that it is a de facto hunt outside of the water. Again, to each their own...
(
Note to Safari first-timers: it has been lastingly acknowledged that standing between an annoyed hippo and water is one of the most effective way to commit suicide in Africa. Hence the rationale for the double...)
Sabatti double. I stand with a comfortable majority thinking and saying that one generally gets what one is paying for. Especially in a double, I would add. There are a number of technical posts on the Sabatti on this blog, with technical details and pictures. I would highly recommend you explore them... Since I referred
Red Leg already twice in this post, I might as well loosely quote him on this: "This is what makes the difference between rifles that last 100 rounds and rifles that last 100 years." 'nough said.