Western AFRICA maybe!

The 416 Rigby is an obsolecent cartridge that has little place in North America. If you are not a handloader, I wouldn't consider this cartridge for a New York minute, because you probably won't find ammo, and if you do it'll cost you MINIMUM $75 a box. If you handload, you can load it for cheaper, but you'll pay a premium for brass.

He asked about a rifle for shooting at longer ranges common out west. Sure, a .45-70 can do it if one is great at doping range and a crack shot, because by the time that big inefficient slug gets out to 300 yards the trajectory looks like an artillery shell. Not exactly a flat shooting rifle. If he hunts up close in the thick stuff, a 45-70 would be great, but in wide open spaces, it loses its luster really fast.

Another less popular and MUCH more expensive cartridge (albeit an excellent one if one handloads or has a lot of money). You have some expensive tastes in rifle cartridges, but I'm assuming that he doesn't have $35-60 to drop PER BOX of 20 for the ammo, and that he's not a handloader.

My suggestion would be to go with a cartridge that is popular enough that you can easily find ammo at Walmart (or similar) and that is cheap enough to shoot regularly to become proficient with the rifle, yet still meets or exceeds your performance needs without being excessivly loud or kick so hard it'll make you a bad shot if you don't practice like crazy.

You've already said that you want to shoot "bigger game," which I take to mean bigger than whitetailed deer, excluding the VERY large and dangerous game like the great bears, bison and such. You also said you want a cartridge "that will shoot longer distances," which I'll assume to mean that you intend to reach out farther than a .30-30 can reasonably reach, which in my mind is 150 yards, but not really looking at shooting at extreme ranges (400+ yards, out where VERY FEW people can take ETHICAL shots on game. Let's face it, most people THINK they are better shots than they are).

Factoring in the conditions in the above two paragraphs, I'd probably choose the following cartridges in this order:

7mm Remington Magnum (7mm Rem Mag, or just 7mm Mag for short): Very popular cartridge, fairly inexpensive, flat shooting and powerful enough to take anything up to and including moose at reasonable ranges (400 yards). Ammo is readily available and the selection of factory bullets for a variety of different types of game is very good. Also doesn't kick too much harder than a .30-06 in most rifles.

300 Winchester Magnum (300 Win Mag): Excellent all around big game cartridge that with the right load will take anything on the North Amercan continent, although I'd probably opt for something a little bigger is my prey can kill me back. Popular and easy to find in a wide variety of loads (though not as common as the 7mm Rem Mag), it does also boast a bit more recoil and will take some practice to master without developing a flinch. Ammo is usually about $18-27 a box in my area, which is pretty good for a .30cal magnum.

.270 Winchester Short Magnum (.270WSM): A relative newcomer, but has become quite popular in the short time since it was introduced. Ammo is not as easy to find at places like Wally World, but it's getting better. Ammo can be easily found at sporting goods stores. Ammo is also not really that expensive. This seems to be an outstanding cartridge for medium to heavy cloven hooved game at most practical ranges. Very flat shooting without a lot of recoil. Also has the advantage of using a short action receiver, making the rifle shorter and lighter than a standard magnum. Handily exceeds the performance of the ever popular .270 Winchester, even in a shorter barrel. With a longer magnum length barrel (24-26") the performance is truly remarkable.

Just my thoughts,

Mike