Beckham was born in the right era I would say. His passing and crossing abilities were incredible, but football has evolved and those attributes alone don't constitute a successful footballer anymore. The defence now has been much more organized and there's little space to pick a cross, that's why teams have to work so hard to stretch the opposition and break a bus. The approach of play has also become much more possession based and there're fewer chances to directly send the ball from halfline to the box.
Some would argue he might play in other positions or adapt to the modern game if he's born in this era. I won't rule out this possibility but I doubt he would be as successful as he was. Modern football emphasizes on all round abilities and he doesn't really fall into that category. In fact, many players nowadays can pick long passes almost as good as Beckham, they are unappreciated just because they have all round abilities and their long passes don't stand out.
In short, Beckham was good in his old days as he was fully fit to the system, but he wasn't that good judging by today's standard.