Would there be any difference in the number of people visiting the sanctuary between Friday or Saturday?

That depends on the time of the year you go. It´s very common to believe that monarchs can be seen better only until February or March. That´s a big mistake. Lots of days of November, December and January are excellent: sunny and bright mornings. Because of this wrong belief lots of mexicanos go to visit the monarchs precisely on February and March. Something foreigners must know is that over 90% visitors to the sanctuaries are mexicanos. And teachers organize their school trips and groups precisely on those months. There are economical reasons for this, aswell. People have expended lots of money on festivities of December and January (Día de Los Santos Reyes, –January 6th), and family pockets recover until February. That´s the time when travel agencies can sell some of this trips. And there comes the “fever” of monarchs.
That´s why even during the week foreigners will find lots of mexicanos and school trips up in the mountains from February on. Something that helps is doing your trip with experts that could avoid crowds, or at least, that have the major possiblities to do it.
In fact, there´s no warranty that you won´t find other visitors, but we recommend this rule to follow: if you´re nearby Michoacán, from endings of Autum till early April, take advantage of distance and visit them. Any way, even in the worst conditions, your spirit will be the winner.