ouch yeah that is a hard one to choose. I'd say that around here, The Rock had a deeper connection with the fans in his hayday than Stone Cold did. They were both idolized by the fans when they were big, thats no doubt. But I'd have to say that The Rock did connect better with the demographic of this area, and so I'd definitely say he was the more popular where I'm from.
However, if I had to choose between which I liked better at their peaks.... I'd go with Stone Cold.
Wow, tough one, I use to be a huge WWF/E fan (along with a pretty big WCW fan) and thought both of these guys were the best year in and year out. The 'Attitude Era', with Stone Cold and Vince going at each other was easily the best wrestling has ever been and possibly ever will be. There are too many good moments to mention, and luckily most of those are either on the RAW Anniversary DVD or on youtube to enjoy again. But The Rock also has his moments - like the funny lines, teaming with Foley and some pretty damn good matches.
But in the end, if I had to pick - Stone Cold gets the vote from me. Without him, wrestling wouldn't be where it is today - it would have faded out in the last 90's, early 2000's.
Overall, IMO, Steve Austin is the greatest performer in the history of wrestling so it's pretty easy where I stand.
The only place the Rock surpasses Austin is the mic work and even with that said Austin is one of the greats in that aspect too. And personally I never thought Rock was that great in the ring, average, but nothing special. Rock's appeal was his charisma.
I have to go with Stone Cold on this one as well, but not by a lot. Both were great wrestlers, both could cut the best promo's or talk wonderfully on the microphone, but I just think that Austin was better because the impact he left in the WWE. I am not saying that The Rock didn't leave a big one either, I just believe that when you put them side by side, then you'll realise that Autin had a better overall career then The Rock.