360 Magnum vs 340 mild street build - my experience

It is not only cubic inches that win here.....
Going back to the OPs idea of 'cam kit & header upgrade', that suggest a good all round performance engine, not a race engine, & that is what my comments below are based on.
The 360 has a lower rod/stroke ratio than the 340. That is a big plus for a street engine. The 360 can use a cam with more overlap/duration than the 340/360 proportion dictates, while having the same idle characteristics as the 340 because the shorter r/s ratio tolerates overlap better.
So the 360 gets a boost from more cubes, but exponentially more tq as rpm increases because of the cam duration increase. All else being equal.