Linear and circular systems should in principle be able to achieve the same water efficiency (within their swept area). They're the same thing - an above ground wheeled mechanism to deposit water.
If you're farming in an area where you're water constrained, then you might not necessarily care about parts of your field not being used (as long as it's reasonably small), since what you care about is your input to output cost.
Some advantages of central pivot is that: a) you only need to feed water to a single fixed point - in a linear system you either need a ditch to draw out of (that's water loss right there), or drag a hose around (that's a possible point of failure) b) you don't need to figure out how to regulate the two ends of your line to keep them in line.
https://www.usgs.gov/mission-areas/water-resources/science/i... has a coarse map indicating a significant difference in practices.
I zoomed in to various areas in the Midwest US, and I didn't see a single use of the circular devices, only square fields which are likely using the linear irrigation device you described.
However, in areas where water is more expensive such as Colorado, I see the opposite: Only circular irrigation devices.
I think what's happening here is that circular devices shoot the water down which causes all of it to land on the crops. The farms in my area generally use a firehose style sprinkler which shoots the water up. This causes a large chunk of water to get lost but it hits the corners of the land. Due to the cheaper water costs in the midwest, this is acceptable.