(a) If any such improvement is finally ordered and constructed, the council shall have power and authority, after the completion and acceptance thereof, to assess the cost of constructing said improvements or any part thereof upon or against the property abutting on any street, avenue, alley, highway, or other public place so opened, widened, improved, lighted, served, or drained or against the property drained, protected or benefited by such improvement to the extent of the increased value of such property by reason of the special benefits derived from such improvements.
(b) If the construction or reconstruction of a system or systems of drainage of swamps or inundated or overflowed lands within the limits of any municipality having a population of 60,000 or more inhabitants according to the most recent federal census, is finally ordered and constructed, the council of said city shall have power and authority, after the completion and acceptance thereof, to assess the cost thereof or any part of the cost thereof upon and against the property elevated, filled, reclaimed, drained, or benefited by such improvement to the extent of the increased value of such property by reason of the special benefits derived from such improvements.