In my experience engineers have more “free time” than eng. managers. As a senior engineer I have not many meetings per week, and the tasks I need to accomplish I can arrange time for them the best way that fits me. So, on Monday I could work fully focused, let’s say, 4h, and call it a day. On Tuesday spend 2h in meetings and another 2h to do PR reviewing… I have almost absolute control over my day, and that feeling is great.
On the other hand, even though eng. managers mostly do meetings, their calendars are usually packed with them. Even worse, they may have one meeting at 8am, another at 12, and another at 4pm… that kills your day completely since you have to stay available during the whole day. Definitely something I would hate.