I would say 4-5 days per week is optimal for most people. When you starting training 6-7 days per week, most people will over train unless they can devote a lot of time to their rest and recovery.
Everytime you train, you elevate muscle protein synthesis. If you train 4-5 days per week, you elevate muscle protein synthesis much more then 3 days per week.
I think 4-5 days per week is that sweet spot.