Managed VS Unmanaged is the main difference (that's why the price difference).
A LW server is supposed to be fully managed, you have nothing to do regarding managing the server (os / panel updates, troubleshooting, restarting failed services, securing etc. etc.) - you just manage your business (and make sure you keep also backups).
A SL server is totally unmanaged, they provide you with great automation tools / portal and you are totally responsible for the server (reboots, make it secure etc. etc.)
Other than that, there should not be big differences on both providers. Both have great datacenter infrastructure and network. Location would also be another difference.
I am a customer of both, and managed vs. unmanaged is the biggest difference.
Along with that (and worth mentioning), Softlayer generally likes to handle all support electronically through tickets. While I have had good results mostly, there has been a time when I went though a huge 3-day headache ticket. I can only conclude that a phone call would have saved all the trouble, since the techs seemed to have a lot of trouble reading the whole ticket and understanding the problem.
On the other hand, LiquidWeb handles e-mail, ticket, and phone support, and their phone support is great and always there.
I do like Softlayer's network better as they are more "central" and generally have lower latencies to most places than LiquidWeb does. In other words, I wouldn't run a game server from LiquidWeb unless I was located in the North Central/Eastern US, but for websites, both of them perform well.