In addition to the better suited sound of the SR60s for your musical taste - the grados are much more bright, bouncy, quick and just more exciting than the Sennheiser HD580s and most other Sennheisers. The HD580s are great headphones in themselves, but for reproducing a different category of music altogether - IMO. The HD580s have a far more refined, reserved, yet elegant sound that matches ideally with classical music, and also they have a more distant sound than the Grado line. But for upfront, high impact, highly exciting sound, Grados are the easy choice, especially considering price and performance.
And in the end you will absolutely need a pretty good amp to drive the HD580s to any degree that the SR60s or any other grado can be driven to good sound. The HD580s without a decent amp can sound quite poor, especially in comparison to the SR60s without an amp. If you go with the HD580s you would end up spending near to $250 and up because you will be needing the amp. But with the SR60s you would probably spend closer to $150 with an amp to deliver even better more explosive sound - especially for your taste of music.
If you can find a store near you with both phones, listen and compare for yourself, the grados will be more suitable for your needs.
Best wishes