Around 1900, the .32 Winchester Center Fire (aka .32-20) was considered a deer cartridge. Currently, .32-20 is considered far too weak for such use.
However, if it used to take deer, it still should, right? What is not mentioned is how many deer were wounded and got away. I think the same can be said for the .30-30 and moose.
One also notes both deer and moose are not considered 'dangerous' game in the same sense as lion, Cape Buffalo and elephant. A wounded deer will not typically attack, like a Grizzly Bear.
I prefer a bit more 'margin for error' with rifles for dangerous adversaries, be they game or belligerents.
My major complaint about the .30-30 is I do not really admire lever guns. Nor is the Savage 340 really compelling. I have a Savage Sportster in .32-20. It is trim and fun to shoot. But I wouldn't use it on deer by choice.