My view: the Golf R stands out more from a GTI or standard Golf, where the S3 doesn't stand out much sitting next to an A3 S-Line. I posted a photo of my A3 S-Line on Facebook and at least 4 or 5 comments were something along the lines of - "Awesome - nice S3" or "Is that the 300hp one?". Those people commenting were not car people...or were BMW/Merc people...but it just shows they couldn't tell the difference.
The same "problem" exists with the BMW 1-Series - I honestly can't tell between an M135i and a BMW 1-Series with M trim - I'd have to look a the exhausts to know. The A45 AMG does stand out but even then if you throw on the Night Pack and AMG Styling Pack onto a standard A-Class then it starts to look very similar.
I also think the Golf R has more boy racer looks, where the S3 is understated and classier. For example I'd happily drive an S3 to a posh dinner party and park outside the entrance - proud of it. But I'd probably park the Golf R further away. Those rims and pipes look after-market.
I'm also a self-admitted badge snob, so despite the more aggressive styling of a Golf R, I'd still have the S3 because it's Audi and it's something to be proud of in any occasion.
The interior makes a big difference as well. I sat in GT-R a few years ago and it's jaw dropping on the outside but the interior is nasty - feels cheap despite the ridiculous power. I get the same impression with a Golf - yes they share the same engine parts etc. but the A3/S3 interior impresses most passengers. The pop-up screen, cleaner centre console, feel of materials, the way the dials click and the glovebox shuts etc.
In that respect I think the S3 (or even A3 if you're comparing against a Golf) is the best all-round package.
Think people missed the point of the article, they've turned the accepted hierarchy on its head as the writer said dynamically he prefers the S3! I've not driven an R, and I firmly believe that even if I did the perceived "better" aspects would be minute - it is after all the same car. I just liked the way it was written and his almost ashamed verdict that he's going against the grain!
Differences are not massive but the cars are setup somewhat different, it depends on what you want. A combination of the 2 would suit. I have driven both and the R is a better handling car and the S3 (saloon) looks better, but it's down to priorities