Much to my surprise, I found examples of royalties used to refer to royal personages in the Oxford English Dictionary. Non-subscribers will hit a pay wall on this link, and the entire entry for royalty and royalties is too long to quote, but here are all the examples of royalties meaning royal personages:
a1592 R. Greene Frier Bacon (1594) sig. F I came to haue your
royalties to dine With Frier Bacon heere in Brazennose
1761 H. Walpole Let. 25 Sept. (1857) III. 441 The late Royalties
went to the Haymarket, when it was the fashion to frequent the other
opera in Lincoln's-inn-fields.
1813 Lady Burghersh Lett. (1893) 51 They are just like the Windsor
Royalties, for they literally know every thing.
1885 H. R. Haggard King Solomon's Mines xvi. 269 This long line of
departed royalties (there were twenty-seven of them).
1902 W. B. Yeats Let. 13 June (1994) III. 207 I will neither mix
myself up with English royalties nor ‘English Soldiers & Sailors’ with
whom the Princess as you say, ‘is so much interested.’
1952 G. Vidal Judgm. of Paris i. 15 He had felt like a royalty
when the man from the Excelsior picked him up.
1998 E. Denby Grand Hotels 213/2 European royalties and statesmen
from America were hotel guests at the time of the funeral of Emperor
Meiji in 1912
The OED (link above) also gives other meanings of royalties; the one of most interest here is (I quote only three examples):
d. In pl. Emblems or insignia of sovereignty. Also fig. Cf. regalia
n.1 2a. Obs.
1607 R. C. tr. H. Estienne World of Wonders 122 This iolly Iupiter
clothed in his royalties.
1769 O. Goldsmith Rom. Hist. I. 39 He assumed a crown of gold..and
robes of purple. It was perhaps the splendor of these royalties that
first raised the envy of the late king's sons.
1863 H. E. Manning Serm. vii. 266 The Vicar of Christ was clothed
with his Royalties
Thus the OP is correct that both sentences in his question are correct. As to which sounds better, to a native English speaker in the US, royals not only sounds better, but royalties sounds incorrect. A speaker of British English might differ, given the quotes supplied by the OP from The Guardian.
It remains now only for someone to find royalties used in People Magazine for me to unconditionally raise the white flag. Well, maybe not. People is not the best example of English usage.