I had the opportunity to visit the Sistine Chapel about six weeks ago ... first time in Rome, and all that. The Vatican Museum was packed. By the time I got to the Sistine Chapel, we were shuffling along in a shoulder to shoulder column. It was possible to step to the side and stop and stare, but the overcrowding is oppressive. I hope the curators can find a solution because the only other option would be to sharply limit access.
I visited a Tut exhibit a few years back. It was mobbed during the day, but you could pay to get a limited access pass for 2:00 AM. There was reasonable number of people in the museum, and it was a lot better to be out in the wee hours than to deal with the crowds at noon.
It doesn't have to be that way. I was also in Rome about six weeks ago. I booked a private guide through Context Tours, which limits each tour group to six people and provide guides with advanced degrees in the subject matter for an academic-like experience. My tour was at 8:00 and included the Sistine Chapel, Vatican Museum, and St. Peters Basilica. When the doors to the Vatican Museum opened at 8:00 am, our guide led us directly to the Sistine Chapel. There was maybe 50 people -- tops -- in the Chapel, including our group, and we were able to sit on the wooden benches, where the Cardinals used to sit, as the guide gave us a "college" lecture that lasted about 35 minutes. When we walked through the Sistine Chapel again about two hours later to get to another part of the museum, the place was packed like a NYC subway at rush hour.