Rosuvastatin tends to cause myalgia less often (2-3%) than atorvastatin (3-5%) in clinical trials. Myalgia is associated with higher doses, 20-40mg for Rosuvastatin, 40-80mg with atorvastatin. Not also can cause some insulin resistance at those doses.
Rosuvastatin is more efficacious at lower doses relative to atorvastatin. 10mg of Rosuvastatin will get 85% of the total efficacy of the max dose. 5mg per day or every other day will also lower lipids a great deal.
Those that do experience myalgia with one can generally tolerate the other as they are metabolized differently. Supplementing with CoQ10 may prevent myalgia from occurring in folks that high intensity exercise.
I wouldn’t avoid statins entirely if I wanted to manage lipids. They work really well. I’d try different combos and doses before giving go up on them.