I have not taken a tour of the Alhambra. I want to caution you about the trade-offs of using a tour there--trade-offs that don't exist at very many other sights.
The Alhambra has several areas with controlled access. You can enter each of those only one time. The biggest one, of course, is the Nasrid Palaces. Another is the Carlos V Palace, which houses a museum I found very interesting. I believe many tours of the Alhambra last only about 3 hours; perhaps some are even shorter. To my mind the Alhambra is closer to a full-day sight than a 3-hour sight. The complex is very large.
From those facts I deduce that if I took a tour, I would not have sufficient time in some key areas and would want to spend more time in those areas after the tour ended. But I would not be able to return to the separately-ticketed areas because of the entry procedures. I would not be able to spend extra time in the Nasrid Palaces unless they happened to be the last stop on the tour (in which case I could just stay inside). My bet is that the Palaces, being the highlight, are visited early during most tours, though I have no information to support that assumption.
Also be aware that the Nasrid Palaces are the most photogenic interiors, and they are always crowded. If someone in your group enjoys taking photographs and wants to include as few stray tourists in the pictures as possible, he/she will need to progress through the Palaces very slowly, maneuvering to get uncrowded pictures. That is totally inconsistent with keeping up with a guide.