Let me apologize up front for the crap-osity of the photos. With only 18 hours of daylight, I couldn't seem to manage to do this in natural lighting. Also, if you're only here for the results and not interested in the method, you can skip to the chart at the bottom.
Before any stringing up, I measured all of the swatches at rest in two points:
I then suspended the swatch from the herb drying line using high tech clipping technology:
I hung a ~250 g plum bob from the corner of the swatch, the idea being to pull on the edge with a uniform amount of force.
This is NOT testing the maximum stretch (the bob is not heavy enough to pull them to the maximum), but rather the 'ease' of stretch. I also tested the maximum stretch, albeit not so uniformly--I stretched the edge with my hands until it would stretch no more. Now to crunch the data. We're not interested in the absolute change in length, but rather the relative amount of change from the original state. The following equation gives us the percent change from the original length (aka percent difference):
The nifty vertical lines indicate "absolute value", which means if the difference between the two values is negative, we ignore the negative sign.
Three values were calculated: The percent change given a uniform force, the percent change to the maximum stress, and the percent change from the 'bulk' knitting to the edge. All swatches were made with k1p1 ribbing. Note that the Knit CO, Cable CO, and Knit BO were done with a needle three times larger than the bulk in order to create a 'loose' CO/BO.
So the conclusion? It depends (the usual hair pulling answer of experimentation). The picot CO and BO certainly have the greatest maximum stretch, but varied wildly from the size of the bulk knitting. If you're interested in a little ruffle at your hemline/neckline/sleeves/etc., that's not a bad thing. The Tubular CO/Kitchener BO pairing had adequate stretch, while also being the closest to the bulk knitting size. For my money, that would be the way to go if you're looking for a professional looking edge with room to stretch.
Got a cast-on/bind-off that you'd like me to try?