JimDandy, the best I'll be able to give you on this one is a hunch. In reading my hunch, please bear in mind that I'm not licensed in NY, and have never practiced there. Accordingly, my best hunch will just be based on general principles of legal practice.
With that said, there are two kinds of "matters to be found" by a court. There are "matters of law," and "matters of fact."
Matters of law -- "That which is determined or ascertained through the use of statutes, rules, court decisions, and interpretations of legal principles." Source:
http://legal-dictionary.thefreedictionary.com/Matter+of+law
Matters of fact -- "That which is to be determined by the senses or by the testimony of witnesses who describe what they have perceived through the senses of sight, smell, touch, taste, and hearing."
Source:
http://legal-dictionary.thefreedictionary.com/Matter+of+fact
Ordinarily, these cases go to federal court, rather than state, and I would expect most of them to be tried to a bench. The reason for that is that the constitutionality of a law is a matter of law, not a matter of fact. In a bench trial, the judge is the finder of fact, as well as the finder of law. When the challenge is simply to the constitutionality of a statute, it's likely that many of the facts (such as "Plaintiff desires to carry a handgun for self-defense") will be undisputed.
In a jury trial, the jury becomes the finder of fact, and the judge is the finder of law. The jury decides whether "the plaintiff actually desires to carry a handgun for self-defense," for example. The judge finds the law and instructs the jury on same.
So, that's the long-winded way of saying: Other than it took [certain parts of] the decision mostly out of the judge's hands giving them a better shot at victory, nothing.
Edited to add: But that's pretty big.