The main advantage of the chain survey over the prismatic compass survey is that the former

Chain surveying and prismatic compass surveying are both used to measure and plot small areas of land, but they rely on different kinds of measurement. A chain survey builds the whole plot out of straight-line distances measured with a chain or tape, combined with offsets taken at right angles to record the position of features away from the main survey lines. A prismatic compass survey, by contrast, measures the bearing, or direction, of each line using a magnetic compass, and pairs that direction with a measured distance.

The critical weakness of the compass method is that its readings depend on the earth's magnetic field, which is easily disturbed by local attraction from iron objects, underground metal deposits, electric cables, or nearby structures. Any such disturbance introduces an error into every bearing taken near the source of interference, and these errors accumulate as the survey proceeds around the plot. Chain survey measurements, being purely linear distances checked by cross-measurements called ties, are not affected by magnetic interference in this way, so the resulting plot is generally more reliable and precise for the same piece of ground.

This is why the main advantage claimed for chain survey over compass survey is that it yields relatively more accurate results, not that it needs no base map, closes perfectly without correction, or uses more portable instruments; in fact chain survey equipment, ranging poles, chains, and arrows, is bulkier to carry than a single hand-held compass.

When comparing two survey methods, focus on what each instrument actually measures, linear distance versus magnetic direction, since the source of error in one method is usually the clue to the advantage of the other.