Look at this graph:
I've owned both the SR60 and the SR80 (but not the i- versions). The graph shows the difference I noticed between the two cans. The 60 has more bass through 100 Hz. It has slightly more midrange presence through 500 Hz. The 80 has slightly more upper midrange between 500 Hz and 2 kHz. Between 3 kHz and 4 kHz, the 80 spikes where the 60 troughs - with a higher spike (5 dB) than the 60's trough (-3 dB). From 5 kHz to 10 kHz, the 80 has the larger spike. This makes the 80 the brighter can. The question is: Do you need a brighter Grado?
Look at this graph:
Comparing the two Grados with the Sennheiser HD600 (a beloved Sennheiser can), the 60 still has more lower bass but the major difference between the Grados and the Sennheiser is in their HF spike compared to the Sennheiser's rolled-off highs. Where the HD800 pulls back 2-5 dB at the high end, the Grados spike as much as 6 dB for the 60 and as much as 8 dB for the 80.
I'm not here to present Sennheiser as the standard. That's not why I brought the HD600 into the conversation. It's just that the Grados offer a clear "house sound" as an alternative to the Senns. The Sennheisers roll off the highs (which allows Senn lovers to crank their cans up louder, for better or worse). The Grados spike the HF, which allows the user to enjoy the music at a lower volume (because louder can grate). The question I would pose is whether you want more spike if you've got plenty of it already.
If you're one of those people who see the numbers - 60, 80, 125, 225, 325 - and readily think that the higher the number the better the sound, by all means: Buy the 80s. That's what I did when I bought my first Grados. I figured, for a few dollars more, I'd get better cans - or at least buy myself some peace of mind. This was back when the 60s came in the S-Cush and the 80s came in the L-Cush. The difference in pads makes a lot of difference, perhaps all the difference. If your ear is right up against the driver, you're going to get more bass and a little less HF. If your ear is pushed a little further away - with no material covering the grill - you'll get a little less bass but a little more HF.
But now, both cans come in the flatter S-Cush pads. This means the differences between the phones may no longer matter. The new SR-80i may have a tweaked driver and/or a tweaked cable (all the Grados are supposed to have gone through driver and wiring tweaks) - but in terms of the cushion, the SR80i is closer to the SR60 than the old SR80.
You might consider taking the difference in price and simply buying the L-Cush pads, which will give you a more open HF. I put more stock in the pads than I do in the numbers Grado assigns to its products.