Grado SR60s are very good phones for the price but the bass improves quite a bit as you move up the Grado line. Bright and harsh I'd say you're hearing a cheap headphone amp. I love Grados but they don't flourish if not plugged into to good gear. Also, make sure you give the Grados a good hundred hours to break in. I agree Senns sound more laid back, but again, good headphones are only as good as the headphone amp you are plugging into. I personally think the highest end Senns are the only ones worth looking at. A friend has Senn HD280s and I wasn't all that impressed with them. I also feel that Senn's headphone cables are shoddy.
I see that you have MTX speakers. May I humbly suggest you are used to hearing hyped bass.
BTW I own Grado SR80s and 225s and have several friends with 60s so I am familiar with them all. Also have a friend who used 12" MTX floor speakers for quite a while.