My wife and I stayed at the Aurelia Residence for 5 nights at the beginning of September.
The staff are outstanding - all of them - and we were really made to feel at home. It was more of a family experience than anything. They went out of their way to welcome us, advise us and be generally helpful.
We were given an upgraded apparment, so it was absolutely huge for just the 2 of us, but it was well-furnished, clean, well-equipped. The kitchen is fine for preparing meals. Somewhat minimal service - room gets bed made/towels changed every day, but cleaned only 2/week and no service on Sunday.
The breakfast buffet is fantastic at this season, on the roof terrace, under the dome of St. Peters.
The negative is the location. It's fine for the Vatican, just 5 minutes walk from St. Peters/Vatican, but it's a bit out of the way for other tourist attractions in central Rome. It's either a 30 minute walk or what we found to be rather an unreliable bus ride (sometimes we had long waits for buses). Suggestion - get day cards (4€) or 3-day travel cards (11€).
Other problem, the railway which runs behind the house. It does generate noise.
I would not recommend the hotel for people who have difficulty walking. The road outside the hotel doesn't have a pavement and it's on a slope.
I would generally highly recommend the Aurelia Residence as good value for money and suggest reserving directly with the Residence for the best rates.