In general, a firm that is operating at constant returns to scale is only going to have cost advantages over a firm that is operating in a situation where diseconomies of scale exist. The firm operating at constant returns to scale is not likely to have advantages over a firm that is operating at increasing returns to scale (where economies of scale exist).
If a firm has constant returns to scale, it will continue to get the same output per input at every level of input. If 10 workers make 10 units of product per hour, 5 workers will make 5 units per hour and 100 workers will make 100 units. There are no changes in output per unit of input regardless of whether the firm grows or shrinks.
Such a firm has a cost advantage in two situations. It has a cost advantage over firms with increasing returns to scale if it has to reduce the size of its operations. It has a cost advantage over firms with decreasing returns to scale if it expands. Thus, it is somewhat more versatile. It is something like a “jack-of-all-trades” that can get by in a variety of conditions.