I've had both at various times over the years, although I don't think I've ever done a back to back comparison. The NAD 3130 is a fine amp, and certainly one of the best I've heard from NAD. It's a nice step forwards from the 3020 but still having its predecessors character and musical ability. I bought one new while at University. I chose it in preference to the also-demmed Arcam Alpha, Rotel somethingorother, and Mission/Cyrus shoebox. The system I came away with was a Manticore/LVX/Basik, NAD3130 and MA R252 speakers. All very pukka Steward/Frankland/Flat-earth maniac recommended kit. And I have to admit, it was lovely. It sang sweetly and kept me awake until all hours devouring all the vinyl my overdraft could stretch to. I moved on to bigger and better things but I still have the speakers somewhere and the amp stayed for years as a stand-in or back-up. What rather shocked me was many years later, with a big an expensive Class A amp that managed to fry itself just outside the warranty period having gone to be repaired (not for the last time either), I dug out the 3130 and was rather shocked to find that I actually preferred it to the big, hot useless lump. The latter didn't last long, although it did manage to fail again only weeks after it returned from a full rebuild. The 3130 stayed on and I only decided to let it go after a posting to the US. The bigger 3155 is similar but with more power. I still have a NAD 7155 receiver, which is effectively a 3155 with a 4155 tuner in the same box. It's a lovely old thing and still serves me well in the workshop. With NAD I think things took a turn for the worst after this series once the "power envelope" thing appeared. NAD amps lost something after that in my view.
As for the A60, there have been so many changes throughout its life that I'm sure an early unit vs. a late one would throw up some distinct differences. I had a beautiful minty early unit and loved it. I recently sold it on because I had just too many amps and I received an offer on it that I couldn't refuse. I also wanted a perfect Naim Nait 2, fully rebuilt by the factory, and that mean't selling off some spare stuff to fund the not-inconsiderable cost. Overall, going on memory, I'd say the A60 has it, and it would be my choice based purely on sonic performance.
Of course, these days a good well-sorted A60 will cost you quite a bit more than a NAD 3130. For under £50 I'd say take a good 3130 over a ropey A60. But if you have £100 to spend then get the best A60 you can find.