The biggest differences are the average level of athleticism is a greater and, of course, the advanced dribbling skills with both hands. Players can get away with carrying the ball and traveling today so that has allowed better separation for shots. Average height is greater and players are thicker and more muscular today. In fact, training regimens are much more advanced as are shooting mechanics instruction.
Racial mix shift from predominantly white to predominantly black or African American over time. As you must know, prejudice was so bad that whites and blacks in the same swimming pool together in the early-mid 60s was rarely seen. The Southwest Conference offered its first scholarship to an African American in 1965 (Jerry Levias) and that was in football. That began to change in the later 60s.
There were great shooters who could have scored in any era: ex. Jerry West, Jerry Lucas or Rick Barry in the 60s; Gervin in the 70s and 80s. Great leapers likewise: Johnny Green or Joe Caldwell in the 60s; David Thompson in the 70s and 80s. Bill Russell could defend and rebound in any era but he was a pretty awful dribbler by today's standards. Bob Cousy and Earl Monroe were ball-handling role models for future generations but would be more average today. Dribbling behind the back was considered to be showing-off by most coaches in the 60s. I got pulled out of a game for doing it (lol). Today, it's done almost without thinking as part of every player's skillset.
The game was much more polite in the 60s with no pounding on the chest, flexing muscles, etc. That was considered bad sportsmanship. Many in the 60s still adhered to the standard of raising one's hand when one had committed a foul. Also, time was not kept to the tenth or hundredth of a second in the 60s so the last minute of games were not managed the way they are today. The early 60s just had a moving hand analog clock, not digital. Because of this change, there is so much more strategy with fouls, clock stoppages and timeouts today than there was in the 60s.
The 80s showtime Lakers, 90s Bulls, the 00s Lakers and Spurs, and current Cavs would all dominate the Celtics of the 60s.
Now, the tough question is if any of the 90s Bulls teams could have beaten the 2014 Finals Spurs. Those eras are much closer together.