I've been playing video-games since the Atari 2600. I had the NES and SNES, as well.
Older games are not necessarily harder, it's just that they require a different skill-set.
Most NES and SNES games were about timing and memory. They used mostly static challenges that required experience to beat. You often had to play--and die--multiple times before you realized the solution and got your timing down. After that, though, it was pure cake. Punch-out is a really good example. It took me forever to beat the last couple of bosses. Once I got down their moves, though, I would beat the game at least twice a day while barely paying attention.
Games now are more dynamic. The same encounter in a game might play out differently from one play-through to the next. It requires more processing power, as you can have enemies come in from multiple directions with a variety of attack options. It requires better decision making skills but less analytical problem solving skills.
Honestly, if you a teenager from the 80s into a game of CoD, they would absolutely suck at it. They'd struggle with The Last of Us or Left 4 Dead. They would have to develop the skills to succeed at games that were outside their experience.
In my opinion, the idea that gamers back then were "better" is meaningless and silly. They were better at the games they played, just as gamers now would be better at the games they themselves play.