No, not specifically. Although half the time I do find myself more in the mood for T1 than T2 which could be called ''conceding'' that T1 is superior.
How often you're in the mood for something or a film's "rewatchability" can indeed be a way someone ranks one film over another but I wouldn't personally. I've watched ROTJ countless times compared to say, FOTR, but part of the reason that I'm not "in the mood" to watch FOTR every other week is because I know I'd be doing the film a disservice if I allowed it to be diminished through excessive viewings. Maybe that's how you are with T2 vs. T1, of course I couldn't say.
But with regard to JP/JW and T1/T2 of course there are many similarities and points of comparison, heck let's take probably the most defining aspects of each respective story: Each is an offshoot of "Westworld" in that humans engineer constructs that end up turning on them and hunting them down and killing them. The central conflict in all three stories, (Westworld/Terminator/Jurassic) involve either a single or small group of people being hunted by constructs from "another era of time" whether it be the past (cowboy/dinosaurs) or future (T-800/T-1000.)
In a biography published in the 90's Cameron stated that he really liked that element of Westworld but that he felt let down by the movie when Yul Brenner's face came off and just revealed some basic gears and pistons that in no way could have been responsible for all of the murderous cowboy's expressions. He stated that because of that the "definitive robot story" had yet to be told.
So we go from Westworld (murderous robots in a theme park) to Terminator and Jurassic Park with each new franchise tackling one single element. Terminator of course taking on the "humans create robots that hunt us down" and Jurassic doing the "humans create theme park attractions that hunt us down." Put 'em together you have Westworld, singularly, you have, well, you know.
Then each series gives us a sequel where the human construct that was a main bad guy in the first film becomes a protector of sorts. And this is where *I* think JW succeeded in spades over T2. In Jurassic World the Raptors, while helpful in a couple key moments, never lose the "yeah, well, they just do what they do" aspect of their carnivorous nature. They never become non-carnivorous or non-lethal. Or at the very least the film was never too shy to show us that lethality in full effect.
In Terminator 2 there's always some massively convenient moment that just sort of "happens" to prevent Arnold from killing anyone *before* John gives him his new "rule" if you want to call it that. Whether it being the 0.0% casualties in the biker bar or John happening to be able to shove aside a T-800's arm before it blows a guys mulleted head off. That kind of "tameness" (in an R-rated film no doubt!) to ME gives T2 a whole new level of "cheesiness" that even JW doesn't reach.
T2 is a crowd pleaser, and sometimes spectacularly so, but I think JW did a better job of "earning" its over the top and/or cheesy moments if you want to call them that.