Well after 10 years of incredible informational arguments from our impressive members the consensus is the reason why the 360 is better than the 340 is because it is cheap.
All things being equal which they never were.
To wit:
1. The better performance engine from the factory was the 340 but the 360 was cheaper.
2. In order to unlock the performance potential of the 360 one must replace the pistons, the heads (or bigger valves like the 340 2.02 intakes), and replace the intake manifold with one such as the 1971-1973 340 intake. These changes are affordable to do because the 360 is cheaper.
3. You can bore the 360 block to its maximum and it will result in the same bore as the 340. Throw a stroker kit on it and you got 408 cubes! Do the same procedure with a 340 block and you get 418 cubes! Everybody supporting the 360 because of its bigger factory displacement should now advocate the 340 block because it now has a bigger displacement than the stroker 360 block! But the 360 block is cheaper to start with.
4. I skipped over the induction changes such as tunnel rams, cross rams, inline dual quads, turbo chargers, blowers, and N2O. The 360 is still cheaper.