People often ask me about visiting Copper Canyon on one of our train tours for Semana Santa, holy week. They have read the accounts of the celebrations there and especially the Mexican mindset really focuses on this time there. To be sure there are some interesting aspects related to the Tarahumara syncretic religious practices. But I have other thoughts and usually inform people of the upsides and downsides of travel at this time.
The upsides are that there are these Mexican and Tarahumara celebrations happening so you can hear the drums, see the Judas dances, and perhaps sample some tesguino. Also if you are catholic, there are special services. Also if your kids are on vacation and you are off as well (everything in Mexico closes for 4 days) then it is a great time to get away.
The downsides are that it is crowded- very crowded. The Copper Canyon train is filled to the gills. So you lose a bit of the Copper Canyon charm. Also I find some of the Tarahumara presentations a bit put on. One other deal is that you have to plan because banks, restaurants, buses–almost everything is closed.
Personally I recommend that of people want to travel in this season, just go the week before semana santa. You still get a bit of the Tarahumara schtick and you avoid the downsides above