First off, a 45-70 should be limited to shots of under 200 yards. With factory ammunition, less than that, more like 150 yards. Longer shots can be successfully taken. However, not everyone is an expert marksman and able to make such shots with hair in the sights under hunting conditions.
The object of the excercise is to take the animal as quickly and humanely as possible with one shot.
The .308 Winchester, AKA 7.62 NATO, is only about 10% less powerful than the .30-06 Springfield, whether factory loads or handloads are used. Used properly, it is quite capable of taking anything in North America, although not ideal by any stretch, and neither is the .30-06.
As far as an all around cartridge/rifle combination that will take any animal you are likely to hunt, save African dangerous game which really requires special weapons and hunting techniques that are NOT the same as 90% of the other hunting in the world, I'd say the 300 Winchester Magnum in a Winchester Model 70 bolt action rifle with a 24"-26" barrel.
I have one, although it is actually a Model 770. The .300 Winchester Magnum can be easily and inexpensively handloaded from the .30-.30 Winchester power level all the way up to my favorite all around load, which is a maximum load for the .300 Winchester Magnum.
My hunting load, which has taken everything from the common groundhog at 400 yards to large Elk at 450 yards, is a Sierra Matchking 168 grain hollow point boat tail spitzer at just over 3250 feet per second. I will not publish the "recipe" for that load for obvious reasons. It is safe and shows no pressure signs IN MY RIFLE. It shoots extremely flat and hits extremely hard. It is also a common load for 1000 yard benchrest shooting in limited classes where you must shoot a production rifle with only a rebarrel and action job allowed and use a production cartridge as opposed to a wildcat.
Shot placement is a requirement for the use of that bullet since it won't smash through massive amounts of bone at long ranges, it is after all a medium weight bullet. Recoil is very manageable with that bullet and load, although it is by no means a mild kicker. It is manageable in that you can shoot 20 to 40 rounds in a session to verify that both you and the rifle are ready to go. It is manageable in that it will not detract from accuracy for the experienced rifle marksman.
You can use heavier bullets, but accuracy simply won't be as good, nor will trajectory be as flat. Since most hunters do not carry rangefinders and shoot their game on flat terrain with zero wind, accuracy and flat trajectory combined with a short flight time due to high speed which cuts down on wind drift are big advantages. Heavier bullets will smash through bone and penetrate deeper on poorly placed shots, but not without the price of less accuracy, less speed, higher trajectory, and longer flight times. Not to mention substantial increases in recoil.
If I had to pick one rifle, to hunt as much game as possible with the best chance of success, a rifle like mine would be the choice. I can easily take ANY North American large game with my rifle and load.
Were I building a new one, and I may, I'd build it like this:
Winchester Model 70 Classic with controlled round feed.
Shilen, Douglas, or Hart 26" semi sporter profile barrel with gain twist rifling.
Simmons 6x24x50 scope.
Action job, glass bedding, and free floated barrel.
And I'd use something very close to my current pet load, adjusted for the rifle's preference.
There are more expensive rifles, barrels, and scopes available, but 999 out of 1000 shooters couldn't shoot/tell the difference on a bet.
