Also being smart about rendering (particularly for web, poorly written animations can run smoothly but kill battery life) can dramatically affect battery life even without affecting execution speed particularly much. They are separate, though closely related, concepts.
1. See e.g. http://www.intel.com/content/dam/www/public/us/en/documents/... p.1 ¶2
I've never seen a case in which getting the work done faster wasn't a win. That doesn't mean it can't happen, of course… But usually vector instructions are a win.
But, if you SIMD-optimize, cheer at how much faster things are, then tell yourself "That means I can squeeze in 4-8x more work in the same time!" Well... You not only eliminated all the Pause time you gained, but you replaced it with high-wattage work.
It takes discipline to optimize for power. Somewhat karmicly, pushing to max out everything can backfire when you overheat the CPU and end up just pushing it into adopting a lower clock rate.
Also take into account memory clock speeds and power on time. Every nanosecond your CPU spends with the memory bus powered up and the memory at top clock, is an important nanosecond.
Make sure your application doesn't idle rough, and executes quickly to spend less time on the CPU, power consumption will follow.