I wonder how the differences came about and how they are reconciled.
The two forms developed independently due to differences of geography and history. Canon law in the West was influenced by Roman law which viewed marriage in terms of contract.
As long as parties did something in public to make a contract, that was sufficient. (Clandestine marriages were always a problem, and another aspect of the issue.)
However, there was a debate in the twelfth century about what the efficient cause of marriage was. Theologians in the “Paris school,” such as Peter Lombard held to a principle of Roman law, Nuptias non concubitus, sed consensus, facit. In Italy, the “Bologna school,” including jurists such as Gratian, held to a principal of German law, that consumation made the marriage. A former canonist Rolando Bandinelli, who came from the school of Paris, “resolved” the issue as Pope Alexander III (1159-1181). He held consent makes marriage, but it may be dissolved for a just cause (e.g., religious vows) before consummation; only a marriage ratum (rightly made) et consummatum (consummated) is totally indissoluble.
However it was the Council of Trent (1545-1563) which began to specify the form of marriage in Tametsi, requiring marriages to be contracted before one’s own pastor, or another priest delegated by him, and at least two witnesses. Before that, such weddings were valid but illicit (in general, I am simplying). Subsequently, the required form went through some permutations until the present.
The Eastern Churches took a different journey with the focus on the blessing which an Eastern Catholic could detail much better and more correctly than I.
The imposition of a form of marriage is by ecclesiastical law and not by divine law. Hence the legislator (the Supreme Pontiff) provides for the proper traditions of the different Churches sui iuris to diverge. Respect for the patrimonies of West and East, I think, reconciles the differences. It’s not entirely dissimilar from the use of unleavened bread in the West but leavened bread in the East. But that’s just a rough use of analogy on my part.