We had visitors this week and for the first time in a 3 years went down to the Colosseo. We have been there 3 times in the past 5 1/2 years; this time was quite an eye-opener. It is a madhouse since the security screening went into effect. Thank you, ISIS. We had pre-purchased tickets at Coop Culture, which gets one into the "skip-the-line" line, but that line was 60-90 minutes long by 9:30AM! There were people selling tours of from 12 people (€18 per person additional) to 50 people (€13 per person additional) that helped our friends get in with "only" a 30-minute wait.
I contacted a guide I trust and have used, Sonia Tavoletta. She does only private tours (€55/hour) and she said that usually she can get people in in about 15 minutes, I do beleive going at opening (8:30AM) is helpful, but be warned and be aware. Buying a ticket in advance from Coop Culture does not save much time. Security is the big problem.
By contrast, the Palatine Hill was peaceful and serene.