I'm with savagefan in regards to the .303 in Canada, it edges out the 30/30 in game downed in Canada, but add the USA and Mexico and it's a no-brainer...the 30/30. I read an article years ago that said, in the old days in Mexico, nobody knew there was any other caliber then the 30/30!!
Consider all the wilderness within the British Empire, or within British influence and we see most of southern Africa, India, Pakistan, the middle east, south Asia, Australia, New Zealand, well, the .30/30 as good as it was doesn't even get out of the gate against the .303. The .303 also has serious limitations and like the .30/30 was used on game that it should of never been used against.
When we talk about house holds that hunted for food by necessity rather than by choice, we are talking about house holds with probably only one or two centerfire rifles. The .30/30 was more popular because a) in some areas it was ubiquitous, and b) it was nice to carry compared to any other rifle. When you are hunting for food by necessity it's not sport any more, and you'll take whatever liberties you have to put food on the table. Today fewer people hunt solely for food. Hunting is recognized as a recreational sport, and as a result has all sorts of limitations placed on it. Fewer and fewer people who hunt are single rifle hunters, and those who are either only hunt deer, or hunt a broad range of game with riles in the .270-.30/06 class. The .30/30 is a great deer rifle cartridge, but to suggest it's suitable for elk or moose, despite having been used for bigger game by thousands of hunters, is to give it more credit than it deserves.
I recall being at the range one day in 1981 or 1982, and an older fellow showed up with a hand made wooden shooting box, with the corners nicely dovetailed together. You could see that he put a lot of time and effort into making that box, and his equipment was immaculate. He pulls out some wooden cartridge blocks, then uncases his rifle and it's a Marlin 336 in, you guessed it, .30/30. That was the day I discovered a .30/30 lever gun could shoot. He shot as well as I did with my bolt gun, probably shaded me a bit, and I have to admit I sulked for a while. But I got over it, (sort of) and gained some respect for the .30/30. But it's still a deer cartridge.