Welcome to head-fi, officially
Alright, let me break it down. Both headphones will do great with either genre. I'm sure others will say that they have a preference for certain genres, but overall it really doesn't make too much of a difference. Not in the sense of sonic similarity, but rather the enjoyment you'll get. After getting used to the sound of each, both will sound fantastic.
Bass is killer on both, but the LCD-2 has more of a kick. Although the HE-500's bass seems a bit faster. Both go deep and have enough quantity for every genre, except maybe rap - for which I recommend Denon's.
I think most people that want to get a LCD-2 or HE-500, usually have to make a difference between the two. Also after getting one of them, I would suspect people either end up getting the other or plan on getting it in the future. No matter which one you get, eventually you'll want the other.
I personally got the HE-500 first due to price. With the HE-500, things are going to be quite exciting off the start. It has far better treble overall in comparison to LCD-2. HE-500 has better imaging and is more wide and airy. The LCD-2 will give you more depth, and a better center stage. It's a bit more smoother sounding overall than HE-500. The mids on both are equal to me along with vocals.
Also based off your current collection, the HE-500 will blow completely blow you away. The LCD-2 is also very good, but takes time to get used to, especially if you have been spoiled with a HE-500 or similar.