I have some Grado 225's, and recently went through an equipment change - Also a friend here has the SR-60's so I've compared them extensively - here's my subjective observations.
I have found that the headphone section in my H/K AVR-320 is pretty lacking compared to the same in a NAD-L40. It should be noted in audiophile headphone circles, NAD for some reason seems to stand out as doing a better job in supplying decent headphone sections in their integrated equipment compared to pretty much everyone else.
That said, I use the 'phones almost exclusively with a Gilmore headphone amp from
headamp and it utterly destroys either of the two receivers (I hadn't ever intended to run the Grado's with the receivers, tried them just for fun, really - I was curious to see if the NAD was really that much better like reports claimed, and it is surprisingly good. The headphones are really for use here at work, and the H/K and NAD pull duty at home anyway).
Also, I was previously using an Audio Alchemy 2-piece transport connected to an MSB Link II DAC and that paired with the Gilmore was pure sonic heaven. I've since sold the transport and DAC and am currently using the sound card in my PC to drive the Gilmore and it is definately a huge step backwards. Personally, I put this all at the feet of the DAC which on the cheap OEM sound card is certainly not as good as the one in the MSB Link II.
Between the SR-60's and the 225's the differences are the 225's have a lot more bass, and are generally just clearer than the '60's, although the loss of the MSB has really 'put the veil' over the sound from the '225s as well. In fact they sound a lot like the SR-60's do now connected to the same gear.
So - I'd say, if you are thinking of upgrading to the better headphones, investment in a better front end will really pay off. The Gilmore design is actually aimed squarely at driving Grado's low impedance headphones, and I think it is well worth the investment (even in the Gilmore Lite which is what I have) if you get the higher-end Grados. That with a decent-quality DAC and you are golden. Driven by the cheap components in the PC, the difference between my '225s and my colleague's '60s are really not as pronounced as they are with better equipment. I should add that this is with the headphone amp still in the loop - without it they really start to sound near identical. I would definately recommend both (decent DAC and the amp) to really realize the improvement over the '60s.