Both are very common, and sound correct. However, it looks like the correctness of the second one could be in question.
CNRTL gives only this (non reflexive) example for arrêter de, and I did not see the reflexive s'arrêter de anywhere on that page:
- L'idée de revoir les lieux où s'était passée sa jeunesse l'exaltait sans doute, car tout le long du chemin il n'arrêta pas de discourir; ... Flaubert, Madame Bovary,t. 2, 1857, p. 130.
LBU, 14ème édition, 2008, accepts s'arrêter de with multiple examples from various authors, without commenting further than to say: "On dit aussi". For example:
Elle me reprenait sans s'arrêter de travailler (Péguy, Souvenir, p. 17).
Même les marins italiens s'étaient arrêtés de bouger (Le Clézio, Etoile errante, p. 202).
So, I would say that both forms are correct, even in writing, by now. I can see how the second one is "questionable": Péguy could have written elle me reprenait sans arrêter de travailler and it would have been the same, because, in the end, who is stopping? There is only one subject here, only one possibility for the subject who carries out the action of stopping. So, you could make a case that there is really no need for that s' in terms of clarity. Removing it is more concise, without any loss. On the other hand, the author might want to add that s', either to underscore who is doing the action, or to soften the expression.
I am adding some preliminary data from ngrams, that needs to be reviewed and criticized (I am very aware that I queried only for the infinitive forms)(the trend is the same for s'arrêter de fumer et arrêter de fumer):