No. The Xbox Series X is running the superior version of this game, hands down. IGN did a technical analysis of this game separately:
As he mentions, it maintains a 1440p count at every single frame he analyzed. It also points out that further patches for the XSX will bring a DRS scaling up to 4K@60fps when possible. It also mentions zero technically measured drops for the XSX in this mode, while it notes there are a few drops for the XSS, and of course, DF offered no technical analysis on this, when in the past they've been very specific, so IGN's assessment is the most reliable, here. The XSX runs just as smoothly as the PS5 at a higher framerate. it's superior.
Furthermore, the most impressive technical version of this game is the 4K native@30fps locked version on the XSX, objectively. That is a 57% superior rendering performance to the PS5's version.