I can give my opinion on all the editions. :)
1st Edition is the grandaddy. It's where it all started. FASA did a great job in a time where RPG's were blooming. They made an enormous amount of splat books but sadly Earthdawn never made the splash that some of their other ideas did. You may have heard of Shadowrun and Battletech. But Earthdawn was their fantasy flagship. The edition itself is pretty solid. It's all there. The setting, the enormous amount of splash, the novels, the big full-color drawings, posters, maps, miniatures, boxed set, cards... They really gave it their all to compete with Dungeons and Dragons. Of course nothing is perfect. ED1 had a few balance issues, something the game would struggle with for a few editions more.
2nd Edition came along, but it was quite a bit of a flop and never came close to the heights of 1st edition. It was made by Living Room games (who had made some excellent splash for 1st edition) and they re-published some material but didn't DO anything. Their forums were a cemetery, whoever was working on it (or copying old content) wasn't communicating, and soon a deadly silence fell over Earthdawn.
But then came the saviors! Redbrick! I talked to a few of the developers there actually, and helped them with calculating some rules for starting at higher circles. These guys were really passionate and the first people to do something with the old game. Of course, by then the game was so old it needed to start over. The old fanbase was getting a bit older and they needed a new audoience, so they started with rebuilding the game but keeping in the core. New art was made, the rules were polished a bit, balance was added, and Classic edition was born. They really did a damn good job. Classic was what 1st edition could ever aspire to be. Lots of content, options, fluff and this time playtested by a core group of enthusiasts. Their forums were a hive of activity and they were great at keeping Earthdawn going.
What exactly prompted them to do so I do not know for sure, but there were some difficulties within Redbrick. Some of the old developers left. Dammi moved on to make a simplified Earthdawn (Earthdawn : The Age of Legend) which I sadly never heard from since, and at some point there was a conversion for Pathfinder too. I think the problem was that Earthdawn failed to draw in a sufficient audience. And at some point, Earthdawn 3rd edition came along.
Earthdawn 3rd Edition tried to do what Classic did but took it further; more balancing and again a fresh start. Some fans thought that some of the charm of the game was lost by making things a bit bland through overly applying the balancing hammer, and some races definitely lost some of their mechanical charm. For example, in 1st edition a Windling could make a perfectly acceptable Swordmaster or Archer due to their 1d10 karma die and massive karma pool. In 3rd edition the race almost completely vanished from all but the spellcasting roles because of their physical weakness lacking compensation after losing the karma advantage. There were other things. In my opinion a well-intentioned edition, certainly playable, but without some of its predecessors charm. They made some new splash that sadly was not overly well received, such as the Cathay (China) supplement.
Then things happened again, and Fasa Games was born out of the ruins of Redbrick (not to be confused with the original FASA). They made 4th edition, and admittedly, it's the edition I've played the least but I see a lot of appeal in. In previous editions there was often a clear 'best' way of building some characters and Disciplines, but 4th edition gives decent options on customization. This allows you to build a character along your own wishes more. For example, a Beastmaster used to be a one-adept clawing machine with some animal traits in most previous editions, optionally with some pets. But 4th edition allows you to collect a zoo of companions, empowering them and then fighting alongside them as a valid alternative. Pretty cool.
Is there a best edition? Nostalgia will have me say 1st edition. Realistically, I think Redbrick's Classic edition is the one my group liked most. But since I haven't really played 4th edition that much, I can't really say for certain that it is the best edition so far, but it might well be.