The court ruled the law unconstitutional. One could say that Group Y won and Group X lost, although it's not clear from the story what role the briefs played in the decision. I don't know what other evidence was presented; I don't even know necessarily that the judges even read the briefs.
But here's the other part of the story. The Northwestern Law Review later published an article suggesting that the court should pay more attention to the claims of Group X than Group Y because Group X had published more articles and had published more in "top-tier" journals.
There is a venerable term for this type of argument: ad hominem.
The article doesn't claim to have found an error in the analysis in Group Y's brief, or pick bones with the way Group Y collected their data. No, the argument presented is we're bigger big shots than the big shots on the other side, so the court should have believed us instead of them. This is by definition an ad hominem argument because the identity of the disputants is made an issue rather than the content of the argument.
The Northwestern article includes this amusing footnote: "In the interest of full disclosure, note that we disagree with much of the information contained in the Millett [i.e., Group Y's] Brief." This is amusing because a full disclosure would have mentioned that not only do the three article authors "disagree" with the Millett Brief, but two of them were actually members of Group X that authored the opposing brief. Instead they present themselves as merely concerned bystanders.
With this in mind, I can't help but be reminded of the ending of the movie Annie Hall, wherein Woody Allen's Alvy Singer rewrites his real-life break-up with his girlfriend Annie as a play, only changing the ending so that Annie comes back to him. To be fair, the authors might be less concerned with stewing over past losses than influencing the upcoming Supreme Court review of the case. I still think their time would be better spent in coming up with more persuasive data and analysis than attacking the reputations of their opponents.