I have an LCD-2 on order at the moment so I don't have extensive experience with them, but I have heard them on several different systems over the last few years and while they don't seem to change as much from simple gear quality differences as the HD600/650 does, they can radically change their sound based on the gear they are connected to. I heard cheaper systems that sounded better than more expensive and backwards again with LCD-2. With the LCD-2 it seems it's more of a game of finding the synergy rather than simply buying 'better' gear.
As to your question about rock, if you like rock with the HD600, chances are you will like rock with just about anything. The HD600 is a generally good all-rounder, but certainly is more geared towards classical, acoustic, vocal, jazz type music where there is more emphasis on accuracy of sound and less emphasis on presence (the feeling of the bass, the sense of space). Rock with the HD800, coming from the HD600, will be much more detailed and have a feeling of being larger. Depending on the recording it could be intimate or a bit further away. Bass will be stronger and deeper, but extremely well controlled. Nothing flabby or resonant. Soundstaging will be more precise, meaning you will really feel like the band is lined up in front of you, playing for you. You will be able to 'see' where each member is standing and likely be able to tell if there is anyone standing behind another person (drums/rhythm guitar/backup vocals/etc). Rock will be exciting and edgy, but not in a painful way, generally. Bad recordings will be exposed, low bitrate files will give you problems. This is all part of the HD800 microscope.
From the HD600 to LCD-2 rock will feel much more solid, more visceral. Bass will have substantially more impact and volume. Bass control is very good, perhaps not quite as good as HD800. Vocals will be clean and smooth, a slightly romantic, human feel to them. The trade off for this solid, silky sound is less detail compared to the HD800, but not too different from the HD600. I feel the LCD-2 is actually more resolving than the HD600, but the overall feeling of detail is similar due to the HD600 sounding brighter. Imaging on the LCD-2 depends greatly on your gear synergy. I've heard these with virtually no center image, and with near perfect center image. It will be difficult to know what to pair them with, but generally I would aim for low output impedance, ultra clean output, and if anything slightly bright equipment. I've heard the LCD-2 on darker sounding gear (of which all were tube amps) and all but one just seemed too dark. The only one that wasn't too dark, was just as dark as the others, but for some reason the overall sound was just so relaxing it sounded very nice. The others were just dark to be dark. I've heard the LCD-2 on a hybrid and solid state amp that were tuned brighter and both of those were where I found the best results. One of those is the Schiit Lyr, which can be in your budget pretty easily so long as you avoid excessive tube rolling.
I haven't seen anyone speak of synergy combinations of M-Stage and LCD-2, but it might work alright. I have seen people mention M-Stage as being one of the best lesser expensive HD800 amps, but have not heard it myself.
Both the LCD-2 and HD800 will be a significant upgrade, and there is really no wrong choice here. The comfort of both headphones is very good with the HD800 being the best I've ever worn and the LCD-2 being merely good. The HD800 is lighter and has more contact area to spread the weight and clamping force. The LCD-2 has thicker pads and is a good bit heavier, but spreads it's weight well enough. The HD800 looks like a space ship and the LCD-2 is not far removed from steampunk. LCD-2 is currently in it's 2.2 official revision. There have been a few non-performance changes since 2.2 officially released that have caused people to unofficially change the revision to now 2.5. The current iteration of the LCD-2 is the most robust, this is the one to get. I recommend bamboo over rosewood for longevity (and looks IMO) but others prefer the risk of the softer wood for better looks (in their opinion). There have been no changes to the HD800 since it was released. Build quality is superb and there have been very few defects, unlike early Audeze versions and revisions. The HD800 is the safer bet if you don't want to deal with any potential flaws.
Edited by Maxvla - 1/25/13 at 10:13pm