I actually own both the HD 800 and the Audeze LCD-3. They are different from each other and I find they complement each other.
The HD 800 does soundstaging better than any dynamic headphone that I have ever heard. The instruments aren’t beamed into your ears they are on a stage in front of you. The effect is amazing. This cans excel with all acoustic music. They are unmatched on jazz or classical music and extremely well-recorded rock and pop.
Their weakness is that they can be a bit bright on some recordings and styles of music. I have paired them with a tube based amp/dac from Red Wine Audio, but on some styles of music they are a bit hard on the ears.
The LCD-3 on the other hand may not match the soundstaging of the HD 800, but it is a superb all around headphone that excels at all styles of music. For me, they are my rock and roll headphones. They handle this music really well without some of the glare of the HD 800.
I would recommend you buy the headphone that matches your musical taste best. If you listen to pop/rock/dance music primarily, then you should go for the LCD-3. If you listen primarily to classical or jazz music, then I would go for the HD 800. In my case, my tastes are eclectic, therefore, I bought both sets of cans.