Two objective criteria
Unless I am dreadfully wrong, the Dakota uses a Win 70 clone action. What this means is that it is a .375 H&H length action with the feeding ramp shortened and steepened to accept the .416 Rigby longer cartridge. This is less than optimum.
Also, the magazine width of the Dakota 76 is designed for the .375 H&H family of cartridges. Fitting the much wider .416 Rigby shell in it is possible, and modifying the feeding rails geometry for it is possible, with good results, but this too is less than optimum.
Therefore, as a first objective criterion, I would suggest selecting a .416 Rigby-sized action & magazine well for a .416 Rigby. This essentially takes out the Dakota.
Further, although it is well mannered in a decent weight rifle (e.g. 10 lbs.), the .416 Rigby already has significant recoil. Even more, if loaded hot toward .416 Wby performance. Screwed-on scope bases are an objective weak link.
Therefore, as a second objective criterion, I would suggest an action with integral scope bases built into a double square bridge. This too essentially takes out the Dakota.
PS: it is worth noting that Dakota offer their factory rifle in .416 Rem (necked up .375 H&H shell loaded to higher pressure to match the Rigby ballistics), but NOT in .416 Rigby. I suspect that the two above points have some bearing on this corporate decision...
Subjective criteria
Aside from the CZ action, which is in a different lower world as a raw product, the two most commonly available .416 Rigby-sized actions are the post-2015 Mauser M98 Magnum and the Heym Express actions. Other custom options exist: Granite Mountain, Mayfair, Prechtl, etc.
Both Mauser and Rigby rifles are based on Mauser barreled actions, so I would say that the pick between a Mauser branded rifle and a Rigby branded rifle is a matter of personal preferences as regard brand, style, finish, etc.
As to which of the Mauser/Rigby or Heym barreled action to prefer, by all reports they are both outstanding...
So, it truly becomes a matter of personal choice. Mauser has its following; so does of course Rigby; and the Heym Martini is built to replicate them.
I too would likely go Rigby, with Mauser in second place, and Heym in third, all for totally subjective romantic reasons...
I would not even consider a Dakota owing to the two objective criteria discussed above.