A couple of years ago we did a B2B Med./WBTA. When in Rome...yes there are crowds with noise, lots of shoulder bumping, security concerns, limited space, etc., but these sites are what they are and can't be duplicated anywhere (Las Vegas tries). We did the Coliseum/Vatican/city tour
DCL excursion. First of all, Rome is a bit of a bus ride from the ship. The Coliseum and Vatican do not allow large bags, backpacks, etc. for security reasons, so leave them on the bus. We got, as DCL often does, a "fast pass" into the fascinating arena (see photo left). There were long lines of folks waiting to enter...we went in almost immediately. It seems rushed, as most excursions do, but you still get some time on your own for photo ops. I would read all you can about these sites before you get there so that the details of your brief visit truly come to life, even with a guide. He/she can't cover it all in an hour or so.
The Vatican was a semi-organized madhouse...per usual. Masses of people want to see all parts of it at once, it seems. Again, no backpacks or bags. Shoulder to shoulder you travel down the many halls soaking up what info your guide can deliver (research the place beforehand so that what you see jumps out at you as familiar). Before we got to the Sistine Chapel we were told for security reasons we would enter it by one of three ways, decided at the last minute. In we went. It was so crowded, literally shoulder to shoulder, I didn't know there were chairs available. Announcements were made to be quiet, which lasted less then a minute, because guides, yes, guides starting to explain more history and facts. A piece of the ceiling had fallen recently, so our guide (a woman who lived next door to the Vatican and was very good) reviewed the current dilemma, replace it or let it go. The heat and moisture from the endless crowds were taking their toll. The conditions for visiting almost any attractions in Europe are hardly ideal, as mentioned above. However, if you want to see the real thing and determine in your mind its beauty, creativity, condition, etc., then you put up with lots of other humans wanting to do the same thing.
While stationed in Germany with the Army from 1959-62 I traveled to 17 countries in Europe. I went to Pompeii where there was a small booth, you bought a ticket, got a map and just walked in where maybe a dozen people were walking the ruins. On the Med. cruise we went there (wife for the first time) and saw loads of venders' tents, huge groups of tourists entering in waves, and controlled routes. I didn't like it, but that is what you have to deal with today. DCL tries to make it worth your while and $$ under less than ideal conditions. As folks have mentioned above, you can spend more one-on-one time with these sites if you hire an outside vender for an excursion (make sure they get you back to the ship on time) or travel ala carte to Europe and take as much time as you like to tour it. Good luck!!
I love maps!) for another 2-3 hours, and I think we spent 10 minutes in the Sistine chapel. 
