You can't compare processor speeds across architectures (in this case X86 vs. ARM). The processor in the old Apple TV was a general use x86 processor. The process in the current Apple TV is a specialized ARM processor for iOS.
You're never going to see A4 to X86 processor benchmarks because there would be no point.
What you say is generally true, however, there's really no harm in trying to find a relatively objective measure of the differences in performance between the processors in the ATV1 and ATV2.
As I mentioned earlier, I think that a lot of the perceived ("seat of the pants") performance gain that has been reported on the ATV2 is the result of the flash memory and the faster graphics engine in that product. However, the A4 CPU isn't really that fast of a processor when compared to "general use x86 processor(s)." Remember, the A4 is optimized for low-power consumption (i.e. battery-powered devices) and while that's a good fit for the current crop of iOS products that fact alone does not make it the best choice for just any task.
Case in point (this may be a bit sobering for the people who are touting the A4's relative performance to the ATV1), here are some Geekbench results for the ATV1 and the iPad (higher is better):
ATV1 (1GHz Pentium, average of user-submitted results): 679
iPad (1GHz A4, singe user-submitted result, other reports are similar): 465
Geekbench tests processor and memory performance, it does NOT test graphics or i/o (which is where the ATV2 may be stronger). These results are for Geekbench 2, but I have no way of knowing whether the benchmark code run on these two different processors and operating systems is exactly alike. However, I suspect that these numbers are representative of the relative strengths of these two processors (integer, floating point, branching logic, memory, etc.).
Here is a breakdown on the ATV1 results (from the most recent ATV1 Geekbench submission which actually reported a higher average of 803):
http://browse.geekbench.ca/geekbench2/view/269530
Integer performance 583
Floating point performance 1077
Memory performance 784
Stream bandwidth performance 660
Here is the breakdown on the iPad:
http://browse.geekbench.ca/geekbench2/view/276786
Integer performance 374
Floating point performance 466
Memory performance 701
Stream bandwidth performance 313
Does this prove anything? No, not really. However, it may be useful when trying to set expectations on just how fast and capable the new ATV2 might be. In any case, in the final analysis it's the user experience that counts and in that regard the A4 and the iOS seem to be doing pretty well.
Finally, here is an article which tries to place some perspective on the relative performance of Apple's A4-based products versus PCs/Macs and netbooks.
http://www.crn.com/blogs-op-ed/the-...s-performance-weak-or-strong-for-its-size.htm