Rerouter,
Summing absolute values is completely different than summing squares. The latter gives rms when you take sqrt of the sum. Which one you want to use depends on what you need, but they are not the same. Squaring puts more emphasis on large values.
Depending on instruction set, squaring (x*x) is likely faster, or at least not any slower than abs(x), hence if you want RMS, you don't even save time by calculating sqrt(sigma(abs)) instead.
If the window from which you calculate RMS is long, the sqrt operation is a small portion, even if your instruction set doesn't implement sqrt. Note, often you just compare things to a threshold, or log it somewhere; in these cases, you don't need to calculate sqrt. Square the comparison threshold instead. Or, calculate sqrt after logging.
On peak detection, do note that you don't want to detect infinitesimally short peaks, otherwise you are just measuring noise. For example, if you sample at 1MSPS, and want to actually detect 1ms peaks, you can average 1000 samples, then detect peaks. So specify your "peak length" first; don't try to detect peaks that are so short that they don't actually appear on the signal of interest.