2010 2.66 GHz 12 core Mac Pro not utilizing all 24 threads?
Solution 1:
It could be as simple as the application you used to test had a resource constraint other than CPU that prevented it from saturating the CPUs. For example, perhaps handbrake was limited in how quickly it could stream data to or from disk. That would limit how much work the CPUs could be given to do. Given that your CPUs will be faster and more plentiful than the older Mac, it isn't a surprised to not saturate the CPUs with the same workload.
I/O contention is used as an example. Without analysis, I don't know what would prevent the CPUs from being the bottleneck. It could be synchronization between that many threads, I/O, a lack of work that can be done in parallel, etc.
Here is a quick test you can use to give the system independent tasks. Open terminal and run the following command. Change the 8 to double the number of CPU cores you have. (double to allow for hyper threading)
for ((g=1;g<=8;g++)); do ( dd if=/dev/zero bs=100m count=10 | bzip2 -c > /dev/null & ); done
Running that was enough to keep my CPU busy for 10-15 seconds. I have a quad core i7 macbook pro. Your CPUs may need more work, so you can change "count=10" to some larger number as well.