Tadić is effective on both sides. On the left he can cross better, but on the right he can cut inside and is far more successful taking on (dribbling) opponents. I'll take two examples from the match against Sunderland. Goal he assisted for Cork is an example of what he does best on the left side, and goal he assisted for Wanyama what he does on the right side.
I would't say he's 'much better' on the left. I think it's clinging to first impressions. He started his first matches on the left, then later spent some time on the right and wasn't as good as he was on the left. But recently he played a lot on the right and was a huge menace every time.
I said left as he can cross the ball in easier. He can cut in on the right, but he doesn't look like an accomplished finisher yet.
Well one thing is for sure. Whether he plays on the left, or on the right, Dusan Tadic makes former Saints player Adam Lallana look ****e.