Forgetting PS4/Xbone and GPU comparisons for a sec, how does the Switch's quad-core ARM Cortex A57 CPU stack up in actual real world, in-game performance versus the CPUs used in Xbox 360, PS3, and Wii U?
Well, it is kinda hard to come along real numbers, as console CPUs are usually only used in console and have no benchmark-runs. It is easiest for the Cortex, because it is a widely used CPU besides the Switch. For instance here you have results (in comparison to A15) for 3 major benchmark-suites (SPECint2000, Geekbench Integer and Geekbench Floating Point):
The Cell was used in supercomputers too, so I see some Linpack-data float around, but that confuses me actually. In Supercomputers you use hundreds or even thousands of CPUs at once, you would have to calculate back to the single CPU. However, here you have an article that uses Linpack and some other tests:
I found nothing on the other CPUs really. But XBox 360 and WiiU both use PowerPC-design (which is also the base of the Cell).
Sadly you can't compare the GFlops in Geekbench Floating Point and Linpack, as Linpack uses just pretty simple operations (matrix-multiplications and stuff like that) while Geekbench uses Real World algorithms (Sharpen, Blur, Mandelbrot). If you want, you can see that the Cell-BE performs in Linpack between 9.67GFlops (1000x1000) to 200 GFlops (Matrix multiplication), while the Cortex does in Geekbench between 2 GFlops (DGEMM) and 6 GFlops (SGEMM). I ignored the ST-results, because that means Single Thread - only one core is used.
This points toward a bigger floating point performance of the Cell (but as I said, simpler operations in Linpack, for real comparison you would use the same benchmark). But this is not surprising, as the Cell was also used for graphics calculations (which are using floating point), while the Cortex in the Switch does the main processing and the GPU calculates the graphics. And the Tegra X1 has a more powerful GPU than the RSX.
I wish all console-makers would do a SPECsuite-benchmark and release the results, these would bring comparable numbers. But they'll never do that.