There are several yet unmentioned considerations:
Given the same movement speed thicker lines fill up a layer quicker, because more volume is extruded per second. In some systems the extrusion flow is the limiting factor for speed, but around corners the print head needs to slow down. Thicker lines = less lines = less corners = less slow down = higher print speed.
Thicker lines have less detail, though. A line of 0.6 mm cannot represent details smaller than that, so smaller line widths capture the input geometry better. Also corners will get rounded by the same distance, so thicker lines = rounder corners.
Thicker lines create worse overhang. Thicker lines require more pressure from the nozzle and if the layer below is (partly) missing the back pressure from the previous layer is less, which results in overextension, which will then also more likely go downward instead of to the sides.
The higher pressure can force lines into small crevices of the layer below, though. This was highlighted by Trish already.
The model Cura uses for a single line is rectangular, while in actuality the printed lines are rounded on the sides. This makes the width of the full extend from side to side larger than computed, at the cost of the corners of the rectangular model. This means that the line width setting should be set slightly smaller than what you would want the lines to end up like.