Performance? Just a recompile with the correct CPU flags? Most likely less than 10%. I"m assuming you are using a relatively common CPU, and in particular you are not using a 32-bit system on a 64-bit CPU.
Power? Assuming that your system is not completely CPU dominated (very few are, even well-tuned supercomputers and large cloud providers only get to 60-80% CPU utilization, most servers and desktops are in the 1-10% CPU utilization range), it will make very little difference. Why? Amdahl's law: Since the CPU is already very little utilized, your power consumption is probably dominated by other things: disk, networking (wireless), display, the fixed overhead of memory and CPU.
Now, if you are running a supercomputer center or a giant cloud farm that uses 20MW, then it might make sense. But you are more likely to have a net loss of energy usage and CPU consumption: You will use more to completely rebuild the system than you save over the lifetime.
By all means, do the experiment and measure, and report back. But if you have anything else useful to do, I would work on other things first. Just getting out of the chair and turning the hallway light off is probably a bigger saving.
