The HTC One XL, which is HTC's version of One X for AT&T, and has the Qualcomm S4 chip inside, instead of Tegra 3, was benchmarked, and it shows very promising results. The test was done with a benchmark tool owned by Qualcomm, which pretty much guarantees that the benchmark results will favor Qualcomm's chips, because they will give higher scores for stuff that only the S4 is good at, and lower scores for stuff that other chips are good at.
This is how it manages to get double the score even of the quad core Tegra 3 inside the Transformer Prime. It's highly improbable the S4 is twice as fast Tegra 3 in any scenario. The new S4 is newer and fast, but it's not that fast. I would agree that in most cases, the S4 should be faster than Tegra 3 by a good amount, while it some it may not be.
For example, all single-threaded applications, should work faster with the S4 chip. Even them multi-threaded ones, who only rely on a second core at most, or they rely very little on more than 4 cores, should still show better performance with the S4. Tegra 3 might still be faster for media-related apps, that need heavy CPU utilization, and might actually use all the cores fully. Browsing might also use all the cores, which is why in some benchmark tests, S4 is about as fast as Tegra 3.
Keep in mind that these are still only benchmark scores, and sometimes they can be very misleading, and the benchmark result could be very different from real world performance. For example it could show 2x higher score in benchmarks, and yet only be 20% faster in real world tests. So it's ok to use the benchmarks as some sort of guiding tool, but make sure you understand what exactly is being tested, and don't rely too heavily on them to tell you which device is faster.