If I just wanted a cheap rifle that would shoot, I'd get the American.
That said to set up an American with a decent stock and trigger will set you back another 500 (B&C stock and Timney trigger)

Technically, the American has a shoulder on the barrel that prevents the barrel nut from screwing on too far ahead of the receiver but that shoulder is of no consequence when assbleing the gun. The barrel nut sits back 2-3 threads from that shoulder when properly assembled and headspaced.

The Savage 110 has no shoulder. The threads just stop. This also prevents the barrel nut from going to far forward. Again, the barrel nut sits back from the en of the threads.

The Hawkeye Rem 700, Bergara, Winchester Mod 70, Weatherby, etc etc DO have a shoulder that mates up to the receiver to set the headspace. This requires considerably more machining and labor to set the headspace properly which is hy these rifle cost so much more than the American or Savage ... Well that and the fact they usually have better stocks and finishes.

If I were looking for a new rifle, I'd be looking for a Bergara in my caliber of choice