Some years ago, I started out with the HD650s. I eventually jumped on the JVC DX1000 bandwagon, and found that they were like the HD650s in a lot of ways but were better in every respect: better detail, better soundstage, more bass definition. I don't even know if they are even being made anymore, but they no longer have much of a following after all the $1000+ headphones hit the market. You might try to pick up a used pair somewhere, as I still think they are good headphones, certainly a step above HD650s. They also really shine with a tube amp. Some peope claimed the mid-range of the DX1000s was wierd or honky, but I never found that to be the case with my tube amps. And Skylab felt the same way.
I own the LCD-2s and really don't think they are all that detailed. Yes, they are better than the HD650s, no doubt, but I actually prefer my JH16s a lot more than the LCD-2s. Sure, the LCD-2s have great bass, but I find them to be a bit rolled off in the upper frequencies. They are also fairly uncomfortable. If money is no object and you want something completely different from the HD650s but much better in every respect, the JH16s would be my top choice.