If you think of pushing pedals like lifting weights it helps kind of clarify the differences in the two different approaches of obtaining power readings.
If your pedaling was bicep curls a single sided meter will tell you how much weight you're lifting and for how many reps, but the accuracy may suffer a little because the meter assumes both arms are lifting equally.
A double sided meter will tell you the same data but will also allow you to see which arm contributed more to the lift and the weight reading will be slightly more accurate.
To me the end goal is pedaling harder and going faster for longer, so a single sided meter gives me plenty to go on. I added it because speed isn't always a consistent way to measure progress since I ride mostly in groups, the number of pulls vary, the routes vary, and the conditions vary.