ARM licenses their architecture designs and others build them. So does Qualcomm. But unlike Qualcomm, there are many ARM implementations, but each Snapdragon is its own model number.
So, if I say, here's an ARM Cortex from Tegra and here's one from Samsung, and they're the same class (A9 as was used in 2012 for example), they'll be mostly the same cpu silicon because they were built under license - but they'll perform just a little differently because Tegra and Sammy roll a little differently.
The Snapdragons use their proprietary Krait CPU cores, not an ARM Cortex design, but they operate on the ARMv7 instruction set (not to be confused with the ARM A7 chip).
Confused? Don't be, you've seen this elsewhere for years - Intel vs. AMD. The AMD will run great, run Windows and your favorite apps because it uses the Intel instruction set, but it's not an Intel design.
The Krait cpu core is an A15-class processor in terms of speed and performance. It's not an A15, just like an AMD chip isn't a Pentium.
The A15 is generally considered to be almost double the performer of the A9 in many circles.
Because the S4 dual core is an A15 class, Samsung thought nothing of providing the dual core S4 in the US while providing the A9 quad core elsewhere on the SGS3.
Samsung somehow managed to break from ARM in one important aspect last year - independent CPU clocking.
The Snapdragon multicores have always run their cpu clocks independently. The A9 dual and quad cores from others ran all cpus at the same speed, whether they needed it or not - not power efficient. Samsung, beginning in 2012, started running their cpu cores independently, like the Snapdragon.
For that reason, some write-ups will call the Sammy chips "like A-whatever (9 or 15)" while others will simply call them "A9" or "A15."
Here's your ARM comparison chart from the horse's mouth -
Cortex-A Series - ARM
Likewise for the Snapdragon -
Snapdragon 800, 600, 400, 200 Processor Specs | Qualcomm
The Snapdragon 600 ought not be compared so strongly to the Snapdragon S4 Pro.
The 600 cores are model Krait 300, the S4 Pro is model Krait 200 cores. The Krait 300 provides 15% faster processing than the Krait 200 when running at the same clock speed.
ARM vs. Krait involves only the cpu cores.
It doesn't involve the GPU, DSP, ISP, media management or other cores - just the CPUs.
Both the Snapdragon 600 and S4 Pro use the Adreno 320 GPU, but it's clocked faster in the 600.
And I agree - benchmarks are pretty worthless for most uses.