Hi sonicdream. It's difficult for me to describe the bass between the two. I will say it like this, the H95 has a little more mid and high bass. Kick drums are more distinct and bass guitars stand out a little more. The iO6 has a more even bass overall to my ears with a slight boost across the board. Sub bass stands out more on the iO6. The bass has more of a 3D, punchier feel to me on the iO6 which I personally prefer. Maybe it's because of the design of the ear cups and the fact that the leather on the iO6 is harder and of what seems to me of lesser quality, but you can feel the bass a little more on the iO6. Neither headphone I would describe as necessarily V shaped, but the iO6 is maybe slightly closer. Where the iO6 really take the win for me is in the Treble response. As a drummer myself, cymbals sound much more natural and accurate on the iO6. The one thing I think the H95s have going for it over the iO6 is that it's a tad more forgiving with poorly recorded tracks. If you'll be listening to lower bitrate tracks, I think the H95s will play better.
In summary, if you will be commuting and traveling with your headphones in any capacity, I would choose the H95 hands down. It has a much better ANC, Transparency, Call Quality, Design, and Look. It also has better features. If you will mainly be using them at home, the iO6 wins in term of comfort (for my head) and sound, just remember, it's a very bare bones headphone. Both headphones work with pretty much any genre including all you listed. If you can live with the slightly artificial treble response of the H95, it's the better headphone overall.