I think that back then, especially flying airmail in singles, currency was usually not a problem because they flew often (duty period limitations were not what they are today).As for proficiency, every revenue flight provided rigorous training challenges. You learned quick, and stayed proficient, or you died on the job, basically.
The safety record was skewed more, I'd guess, by lack of timely, accurate weather information, and of course equipment limitations (including things like "improvisational" maintenance and poor or nonexistent charts) than by a lack of formalized recurrency training. No doubt those guys were very good at reading the sky, etc., but assuming they felt compelled to carry on when things didn't look very favorable, they were pretty much asking for it. Those "early birds" also needed very good basic nav skills, and the ability to deal with all manner of mechanical problems.
St. Ex was mentioned earlier: reading his accounts of flying the mail in overworked, primitive singles, in just about any weather, at night, over the Andes (!) suggests that all of those guys were completely insane. I'm not sure how any recurrency training we use today would have helped them much. Only the very best learners survived to retire... assuming they also had incredibly good luck. But he also talks about very strict adherence to the simple procedures they used; his own diligence and consistency helped keep him alive during those flights.
Nowadays we sometimes see commercial pilots choke when they are dealing with a nasty surprise outside the safety of a simulator, or confronting something never run by them in the sim. And sometimes we see them pull off some miracle that would make an old airmail pilot smile. Some pilots are just more diligent- and luckier- than others... that hasn't really changed.
I'm not dismissing the obvious benefits of systematic training, CRM, etc; just pointing out that in the end, it's not about that stuff any more than it is about good airplane-handling.
So the poll question is definitely an apples/oranges comparison... "better" pilot means "pilot with better judgement", if you ask me. Stick'n'rudder skills, extensive knowledge, and even modern recurrency training techniques do not outweigh good command capability.