It honestly depends on where you live.
I don't feel any safer today than I did before 9/11 unless I'm in Manhattan. I will say if you're a gang member you gotta be way more covert. Pre-9/11 you could be a big ass gang holding meetings inside of a church and nobody could do anything about it. Now the city is quick to crack down on anything with little restrictions. For a while it felt a lot safer, but then stop & frisk made tensions grow more. Some things got better but because there was so much worry about keeping Manhattan safe, it came at the expense of everywhere else, and no borough is farther away from ground zero than mine.
Day to day life in the city didn't really change because I had paranoid parents who worried about my safety, but that's a product of living in the hood, not so much 9/11. My mom on the other hand is afraid to be in large crowds alone. We went to ground zero 2 months after the attacks and she didn't dare go back til 2 years ago.
Initially, New Yorkers were nicer and it showed when the 2003 blackout hit. Everyone was nice. We talked to our neighbors. It was easier to talk to people because we were too busy watching out for terrorists to worry about potential creeps. Any time something big was happening, first thought was terror attack. Now we've gone back to instantly blaming random dumbasses handling street shyt. We're slowly getting back to not giving a shyt about each other but I think that's a result of other issues, but every once in a while, NYC will play nice for the cameras.
I was a sophomore in HS when 9/11 happened. Of course life is different now. Covid has done more to affect day-to-day activities than at any point during the attacks. I always have awareness of where I'm at and who I'm around but that's a byproduct of needing to keep your guard up in the hood. While a lot of people became frightened and uncomfortable, post 9/11 life was an easy adjustment. We're on edge already.
if 9/11 didn't happen, things would be a little easier in that they coulda reallocated money devoted to counterterrorism, but 9/11 also offered opportunity for a lot of people. The city wanted to build shyt once the Twin Towers went down and my dad worked construction. There was a job open everywhere for him. It wasn't just 1WTC that popped up. There's giant skyscrapers everywhere. Some still aren't finished. Now we're gonna see skyscrapers in Brooklyn. Queens will get another one. So many neighborhoods got redeveloped. The downside of that is course, gentrification and the cost of living skyrocketed. 9/11 started the "let's just redo this whole neighborhood over" movement and BK and Harlem were the first targets.
I can't answer whether NYC would be better or worse. Something would have caused the shift we see today, but damn, 9/11 expedited a lot of stuff. Otherwise, business as usual in the Bronx.