There are lines to collect your reserved ticket. Those lines (there are several) could be longer than the line to buy a ticket without reservations... Unless, of course, that morning is booked solid. No line there at all, meaning disappointment for those without reservations, could be a possibility on a Monday.
Museums that are at their reservation capacity will be crowded. But in Europe, I think it's typically better than in the U.S. For instance, we saw a popular Impressionist Exhibit at the de Young Museum in San Francisco... o_O ... Their idea of sold out was even more claustrophobic than free day at the Prado in Madrid. Yes it's a small place, but getting up for a good view of 'Starry Night on the Rhone' was like being in a mosh-pit at CBGB's in the '80's. While in the massive Prado Museum on a free evening, there were only a few dozen people crowding around 'The Garden of Earthly Delights'.
To compare the Vatican Museum, 'Fire in the Borgo' is in a fairly small room, but since it's mounted rather high, I was able to stand in the middle for quite a while and enjoy all the Raphael's without feeling too squeezed. And in the Sistine Chapel, it was ear-to-ear, but I still found a place on the steps to sit awhile. (I'm pretty sure there were signs saying no sitting, but at least 60 people were doing so.)