Interesting article! As a Scot who lives here for a few years, but observed under some good skies for 20 years in highland Scotland (very dark, but cloudless <<50% of the time), the Southern sky wins on most, but perhaps not quite all, counts. Others have rightly complimented the South, so I'll stick up for a few of the North's sights
The things I miss from the North:
Galaxies and galaxy clusters -
apart from the LMC and SMC, which are amazing and unique, I think the North still has the better of the brighter galaxies and galaxy clusters in the sky, including such treats as M101, M51, the Virgo Cluster, Andromeda & Triangulum, and lots of other bright galaxies and groups around in Leo, Canes Venatici, Ursa Major Coma and elsewhere. By contrast, many southern galaxies are isolated and fairly sparse, though there are obviously some good ones (NGC1566/Dorado, NGC253, M83, Fornax spring to mind). The southern Galactic Pole also lacks distinctive constellations in comparison to the north.
Planetaries and SNR: I'd be surprised if there were more planetary nebulae in the north, but perhaps the best two visually are the Ring and Dumbell (the Helix is quite dim in a scope, though excellent photographically) are northern treats, along with clearly the brightest supernova remnants, the Veil and the Crab.
Being from Scotland, I miss the accessibility of the mesmerising
aurora, and also the summer
noctilucent clouds, neither of which are very visible here. Though the lack of full darkness in summer would bring tears to the eyes of many a deep-sky observer!
But just to twist everyone's tails - the constellations are the wrong-way up here, and the Sun, moon and stars *definitely* move the wrong way across the sky

. Orion on his head?? Leo on his back?? Even Scorpius is upside-down


. Many northern constellations are more distinctive patterns IMHO, making basic sky navigation easier. And we have a Pole Star

.
The North has a terrible deal with the way the Milky Way is tipped - the galactic centre well to the south and a big fat dust cloud through what would be otherwise bright bits just north of the centre. The Great Rift through Serpens Cauda, Aquila and Cygnus probably hides a lot in comparison to the treats of Carina, Crux through to Norma, a similar distance the other side of the Galactic Centre.
Oh to come back in 13,000 years when precession has made Sagittarius and Scorpius northern constellations, in place of Taurus and Gemini, then the discussion would be a little different!! Though the LMC & SMC will remain in the south, and the Virgo Cluster in the North, being near the Ecliptic Poles.
But the weather is, by a huge margin, better for astronomy in Australia. Dry, clear skies for a huge proportion of the time are precious for astronomy, quite apart from all the great stuff you get in southern skies. For astronomy, I'd live in the South. But I still look wistfully north for just a few things