Not a noise free, but the difference is HUUUUUUUUGE. You can make a test. Take a pic with ISO 1600. Look at DNG and JPEG. The difference is really something. Not only noise, but the colours too. And it's not about postprocessing.
Sorry, man, I have a Lumia 925 too and 930 is better in low light if you use the SAME SETTINGS. That's the problem with auto mode, Lumia 930 tends to use ISO 1600 or higher in some situations, which is veeery bad. The aperture size on 925 only brings a lot of unnecessary noise.
I can prove if you insist. I can take low light pics now if you want! I have both with me.
And yes, like I say before, Lumia 1020 have more detailed pictures, but I definitely wouldn't change this for better colours and better dynamic range. But it's me. The great thing on Lumia 1020 is the Xenon Flash. It's reaaaaally awesome and make big difference, inded.
Here the 925x930 comparison I made (I made it very quick, sorry for 4:3 x 16:9 and not very accurate angles)
http://1drv.ms/1tHNAIM
A little example:
925 ISO 800 1s
http://abload.de/img/wp_20141009_21_54_46_1zjm9.jpg
930 ISO 800 1s
http://abload.de/img/wp_20141009_21_53_58_imkup.jpg
So there's no such thing like "925 is better for low lights because the aperture size". The difference is only that 925 have a bad post processing changing black shadows for green shadows. This problem also happens with Lumia 920 or Lumia 1020.
So this is why I think 930/1520 have the best Lumia camera for now.