I have taken both a Perillo tour (2002) and multiple RS tours (11 and counting). My thoughts will echo many of those posted by Alan, but here goes!
Would you rather be lead around by a guide with 50 people or half that number? With Perillo, you'll follow the umbrella as one of many, recognizing some of your "family" (that is what we were called on our trip), but with RS, you'll be in a group of about 24-28 people who you will meet and talk with and maybe even pal around with during free time. People mixed with each other more with RS than with Perillo.
Do you want to know the price before you take your trip or not? With RS, the price is up front and the only extras are what you choose to do on your own. With Perillo, early on the guide will discuss all the extras and the additional costs ($50-$200 depending on the excursion). That can add up.
Do you want to go-go-go or take it easy? Both give you the option of skipping activities. With RS, typically there is free time built into each day (less so on traveling days) and it is your choice on what you want to do with the time. Some enjoy sitting and people watching while others prefer to see as much as they can. And while you can do some of that with Perillo.....
Do you want to learn how to use local transportation and have your hotel in a location where you actually can get out and see the sights? This is one of the biggest decision points for me. Perillo often will have your hotels farther out from the city, in hotels that are more corporate/generic to appeal to the masses. RS will use smaller, centrally located hotels, filled with quirks. Some people like that and others don't. The RS guide will give an orientation walk, showing you where and how to take the bus/metro and how to navigate and stay safe. With Perillo, people just stayed with the group and guide and didn't venture far away (not that they couldn't).
Agreeing with Alan on the rest of his points. :)
Hope this long-winded post helps you decide!