I have the Savage Edge (Axis) and the Remington 770. Savage is 22-250 and the Remington is 30-06. The 770's have been slammed on the internet for a long time.
My personal experience with the 770 is the box magazine just doesn't look like a real smooth fit along the bottom of the gun, but it works flawlessly. The bolt on the 770 is a bit rough from the factory but after working it a bit it smoothes out.
In my book the Axis would be the preferred cheap gun, and after that the 770 due to the detachable box magazine. I won't own a gun without one.
The 770's stock is more robust compared to the Axis on my 2 guns. No flex on the 770, although I don't have an issue with the Axis. The way the 770's stock is shaped with the shape of the trigger my hand feels like it's molded right in there.
Trigger from the factory goes to the 770 for a lighter pull, but I lightened up the Edge trigger for $0 to where it rivals my accutrigger.
Safety position and feel goes to the Axis. Remington is ok, but the Axis has a nice big thumb sized switch.
Accuracy is a wash. The Remington is very consistant and that's with the cheap scope that came mounted on it. I shoot the 22-250 more just because of the recoil issue with the 30-06. I have shot 1 inch and less groups with the Edge but to be honest I only shoot the 770 at the beginning of deer season to make sure it's sighted in. 2 shots is the most I can take in a row but they are normally within a half inch of each other.
I would expect the Axis in 30-06 would jolt the shoulder pretty well too.
Neither one will be something to pass down for generations.
Both will kill game.
Owning both, if I was looking for an entry level rifle I would get the Savage Axis and never look back. Best value for the money out there.