Objection 1. It would seem that an oath is more binding than a vow. A vow is a simple promise: whereas an oath includes, besides a promise, an appeal to God as witness. Therefore an oath is more binding than a vow.
Objection 2. Further, the weaker is wont to be confirmed by the stronger. Now a vow is sometimes confirmed by an oath. Therefore an oath is stronger than a vow.
Objection 3. Further, the obligation of a vow arises from the deliberation of the mind, a stated above (Question 88, Article 1); while the obligation of an oath results from the truth of God Whose testimony is invoked. Since therefore God's truth is something greater than human deliberation, it seems that the obligation of an oath is greater than that of a vow.
On the contrary, A vow binds one to God while an oath sometimes binds one to man. Now one is more bound to God than to man. Therefore a vow is more binding than an oath.
I answer that, The obligation both of vow and of an oath arises from something Divine; but in different ways. For the obligation of a vow arises from the fidelity we owe God, which binds us to fulfil our promises to Him. On the other hand, the obligation of an oath arises from the reverence we owe Him which binds us to make true what we promise in His name. Now every act of infidelity includes an irreverence, but not conversely, because the infidelity of a subject to his lord would seem to be the greatest irreverence. Hence a vow by its very nature is more binding than an oath.
Reply to Objection 1. A vow is not any kind of promise, but a promise made to God; and to be unfaithful to God is most grievous.
Reply to Objection 2. An oath is added to a vow not because it is more stable, but because greater stability results from "two immutable things" [Hebrews 6:18.
Reply to Objection 3. Deliberation of the mind gives a vow its stability, on the part of the person who takes the vow: but it has a greater cause of stability on the part of God, to Whom the vow is offered.
Source: Summa Theologica (New Advent)