Directly correlated no, as Vautrin and Wriothesley do not share any sort of deep relationship and they don't depend on each other for there to be substance for each respectively. If you're asking me if there's parallels between them as characters absolutely there's a few within the canon setting of the game.

• Vautrin enacted his own justice against those who forced Carole into her unfortunate fate. Wriothesley enacted his own justice against his foster parents who treated him and his siblings like cattle.
• Both committed their crimes in the name of those they championed as family. Vautrin saw his little sister in Carole (Vautrin's sister had since passed away). Wriothesley had his siblings.
• Both were failed by the justice system in place in Fontaine, both in their respective times of date. Since Vautrin has long since passed given the timeline.
• Vautrin and Wriothesley share a special relationship and bond with the Melusine. There is a respect both have for the Melusine. An attachment.
• One can surmise that both Vautrin and Wriothesley may share an identical form of thought. Traces of this can be found in the Mutual Aid Network which was formed by Vautrin and in the way Wriothesley tries to run things in the Fortress of Meropide.

My view on those two is the same one as what Vennessa is to Jean and Nabu Malikata is to Nilou, a rough comparison since Vennessa and Nabu Malikata are quite lore prominent but you know what I'm trying to say right? They are but mere echoes of the past in a new samsara since we're all too familiar at this point by how important "time" is in this game. I hope this answered your question, I appreciate you asking.