The Stele of the Vultures, from the Early Dynastic era, was discovered at Ningirsu and depicts the Lagash king Eannatum. The reverse is primarily religious and shows the king's nocturnal vision, implanted in his head by Ningirsu or his mother Ninhursag: the god beats the head of a prisoner, bound up in a battle net with other captives, while his mother stands behind him to grant addition divine approval. The obverse is primarily political, showing the prophesied battle in a glorious climax while the king engages in various warrior activities.
Unlike the purely religious narrative of the Uruk Vase, the Stele weds the religious and the politics; also, the Stele depicts the king in various poses and settings. While the Vase showed the city ruler as part of a greater assembly of priests, the Stele narrates the preface and climax of a victorious battle where Lagash crushes Umma.
By means of a religious and political narrative, and by showing the king as a direct liaison to the gods, the Stele shows an evolution since the Uruk Vase, with the king now being a ruler bearing divine approval, carrying out actions dictated by the gods and engaged in battle for his city.
This fits into the larger events of the era, which saw city-states entering into conflict over the irrigated farmland between them (typified by the Lagash-Umma border conflict itself). Thus it makes sense that the nature of kingship and divinity would have adapted in the way captured by the Stele; that is, the king would become a military leader by virtue of the city god who blessed his pious earthly underling with sanction to battle and an ensuing victory over his enemy.
Crawford, Harriet. 1991. Sumer and the Sumerians. Cambridge: Press Syndicate of the University of Cambridge. (Page 246-9 sheds light on the stelae.)