Yeah the 86 Celtics would stomp any version of LeBron's Heat. Not the same as saying Bird's better than LeBron, though. Which is also not the same as saying Bird accomplished more than LeBron, which is probably the fairest way of assessing this sort of thing and is tilting increasingly sharply in LeBron's favor.
I'm not sure that accomplishments are the fairest way to settle things without evaluating the level of competition a player played against. Those Lakers and Sixers teams that Larry lost to were legitimately great teams. I don't think any team in today's era rises to that level other than the Heat, and the aging Spurs.
I meant individual accomplishments too, but part of my problem with evaluating teams like that is that a big part of what makes a team "great" is winning championships, and all-timers tend to snap a lot of those up.
If Jordan never played or never got a decent team around him, the late 90s Jazz would probably be a "great" team today; because Jordan got in their way they aren't. If OKC had beaten Miami 2 years ago they'd probably be "great" already, but instead they're not there yet. Conversely, if we'd won Game 7 in 2010 LeBron beating us in 2011+2012 would be more highly regarded.
Extraordinary players and teams tend to make everyone else look more ordinary in comparison, which later makes them seem less extraordinary because the competition isn't as highly regarded. And that's without factoring in the biases fans and the media are always going to have, which clouds things further. We had a Miami fan in here a couple days ago dumping on the level of competition Russell's teams went through; naturally we Celtics fans didn't buy it for a second. Relative to the league they played against seems cleaner to me. But that's the fun in this kind of debate.