I own the A900, so I can only comment as to my opinions and experience with these cans, which I've had for a year or so.
With respect to the bass, these cans pack a punch. The bass is powerful, pretty tight, but sometimes at least for my listening preferences it can be overpowering especially depending on the type of music and recording. Mind you I am not a big bass head.
A900 have a very good soundstage so I assume positioning for games would be quite good as well.
They are easy to drive so no amp is required.
And are closed cans, which will reduce outside noise; and wouldn’t annoy others while you are gaming or listening to music.
I might also add that these cans are very comfortable and extremely well built, probably better than the 595.
With respect to different types of music, I am quite happy with the A900 for all types of music—rock, rap, pop, jazz, and classical. But feel guitars either electric or acoustic sound very good, but miss that little something extra. This is noticeable or less noticeable depending on the recording or track. I also think that sometimes vocals, depending on the recording or track sound a little nasal. But I am being very critical.
I think either can will be a very good choice, but the 595 might sound a little better (if you have an amp) whereas the A900 will probably have a better soundstage (an amp wouldn’t make much difference).
Here is a link for the A900; if you look to the lower right it rates the different types of music:
http://www.h-navi.net/a900.htm
Here is a link for the 595; if you look to the lower right it rates the different types of music:
http://www.h-navi.net/hd595.htm
I don’t know how accurate these subjective ratings are and there are a lot of variables involved, but in my opinion they are a little biased in favor of any Sennheiser model.
It should also be noted that the HD595 benefit greatly from an amp, but probably are easier to drive then other Sennheiser models.
Without an amp, based on my recollection I think the A900 might be a better choice.
Best of luck