In terms of methodology, the problem, of course, is that the 808 PureView is designed from the ground up to deliver 'pure' images at 5MP, with a 'creative' option to capture raw 34/38MP images if you 'know what you're doing'. Whereas the G4 shoots a high end but static 16MP image - so how best to compare the two?
One option would be to pit the raw 34MP images from the 808 directly against the G4's output, with higher resolution and never mind the disparity in framing. I've done one shot like this below. The other option is to recognise that Nokia were onto the right idea in capping the output at 5MP, already exceeding the resolution of all known displays at the time and still 99.9% displays today in 2015. With this in mind, the other data points below are compared by (bicubic) downsampling the G4 output to 5MP - this is, on the one hand, a little unfair to the G4, but then almost no one is ever going to see the pixel detail at 16MP in real life, and besides, the G4 still comes out of the comparison very well overall.
Test 1: Bright sunshine, massive landscape detail
In this case, all the texture and detail on my local church. Here's the full scene, for context:
And here are 1:1 crops from the Nokia 808 PureView (top, at 34MP) and LG G4 (below), click either hyperlink to download the full original JPGs for yourself, for further analysis:
There's clearly more image information in the 808 photo, thanks to the much higher resolution, though the G4 does very well, with detail that's sharpened a little but not excessively so. In contrast, the 808 image is quite deliberately neutral in terms of processing - there's no sharpening whatsoever - that's left - in this 'creative' mode - to the end user, doing what they want with the 10MB JPG file.
We're not really able to compare like with like here, but I'd venture to say that the G4 isn't far behind overall, which is impressive considering that its sensor is around four times smaller (albeit that the aperture is about twice as wide, so there's some cancellation of effect here).
Test 2: Indoors, average light
Brochures in my local bank, shot at about 1.5m. Here's the full scene, for context:
And here are 1:1 crops from the Nokia 808 PureView (top, at 5MP) and LG G4 (below, from 5MP downsampling), click either hyperlink to download the full original JPGs for yourself, for further analysis:
With the caveat about the G4 being done a slight disservice in reducing its resolution, I'd give a slight win to the Nokia 808 PureView here, in its comfort zone and able to use its fast hardware oversampling to reduce noise and home in on detail. But there's very little in it overall.
Test 3: Outdoors, shady macro
Trying to get close to some nice bluebells in the shade in the corner of the garden. Here's the full scene, for context:
And here are 1:1 crops from the Nokia 808 PureView (top, at 5MP) and LG G4 (below, from 5MP downsampling), click either hyperlink to download the full original JPGs for yourself, for further analysis:
Note that the framing of my crop is deliberately different here, in that the Nokia 808 just couldn't focus close enough to the lead bluebell - so I've shown a crop that demonstrates that the bluebells behind were at least in focus. The G4 had no problems getting very close, with an impressive shot all round.
Test 4: Party time!
My typical party mockup, with an amateur at the controls (a family member) and with me deliberately trying to keep moving - as someone would at a typical party or event. The distance was about 1.5m, again typical of how you'd shoot down the pub, for example. Here's the full scene, for context:
And here are 1:1 crops from the Nokia 808 PureView (top, at 5MP) and LG G4 (below, from 5MP downsampling), click either hyperlink to download the full original JPGs for yourself, for further analysis:
The G4 image isn't as bad as some phone cameras I've tried, but there's definitely far more to work with in the 808's case, with almost complete freezing of motion - look at the bottle label, for example.
The 1.5m distance is kind of on the edge of even the Nokia 808's Xenon flash range, but there's enough frozen detail captured that 10 seconds 'auto-tweaking' in a photo editor on the desktop gives:
Which, considering that I was (deliberately) moving significantly and that my family member may not have had a rock steady hand, is a pretty impressive result for my typical 'party' ad-hoc snap from a phone camera.
(Bonus) Test 5: Oversampled sunshine
I got so many complaints about using the raw 34MP photo from the 808 above rather than using the oversampling, I've done another data point. To aid comparison, I've downsampled the G4 shot to 5MP too. A little unfair, but it shows off the image processing from each phone camera well. Here's the full scene, for context:
And here are 1:1 crops from the Nokia 808 PureView (top, at 5MP) and LG G4 (below, from 5MP downsampling, the link is to the full 16MP version), click either hyperlink to download the full original JPGs for yourself, for further analysis:
As people have pointed out in the comments below, the 808, when oversampled in PureView fashion, still produces stunningly clear and natural results, while the G4 looks immediately sharper, even when scaled down like this, but is just on the edge of appearing over-sharpened. Given that I've been unfair to the G4 in terms of resolution, call it a score draw overall!
Verdict
Only five data points above, but enough for me to hazard an opinion that the LG G4 and Nokia 808 PureView are pretty close in terms of results overall, and indeed in terms of experience, with the 2012 808's lightning fast hardware-accelerated oversampling being matched with the raw processor oomph of the G4 from 2015. Where they differ from an imaging point of view is in their specialities - the G4 is much better at macro shots, has OIS and can do auto-HDR very effectively, while the 808 still produces 'perfect' images at 5MP, has a real Xenon flash and isn't afraid to use it indoors and in low light.
I'd say 'place your money and take your pick', but then 808 isn't even sold anymore and goes for silly money second hand. So it's all a slightly moot comparison. I reckon the 808 PureView still holds up quite well even against the 2015 imaging powerhouses, all things being considered, though from a smartphone point of view the ageing OS and apps make it a very poor relation, of course.
Comments welcome!