Rosuvastatin is hydrophilic, doesn't cross the blood brain barrier and is more efficacious at lower doses than atorvastatin. Atorvastatin was the first "high intensity" statin and the thing that doctors tend to push.
I much prefer Rosuvastatin in lower doses in combination with other lipid lowering compounds. Theoretically, Rosuvastatin would have fewere adverse side effects than Atorvastatin, but the data don't show a lot of difference. There are reasons for this, not least of which is that most people on statins are on the max dose. Pravastatin is less efficacious than Rosuvastatin, but at equivalent doses, has fewer side effects.