Right, I should be able to answer this question as I was training as a Service Controller (similar to air traffic controller, except for trains) for the Circle line, but quit that job as it didnt pay enough and gave me my first white hairs.
The circle line, during the rush hour will always be slower due it sharing tracks with the Metropolitan, H+C and District lines and the congested timetable. Give yourself about 25 mins for the journey plus 10 mins waiting time (just in case there are delays or train cancellations).
There is no need to make any interchanges. Liverpool St to St James Park is a single ride on the Circle line.
So why does the Circle line always seem to sit at Edgware Road? Because that is where the driver depot is and is where driver changes happen. On top of which it hjappens to be a MAJOR junction, all controlled by a very old signal cabin (those guys really do work for their money), so there is always a lot going on there. We also reform trains at Edgware Rd, which means trains might be changed from Circle to H+C and vice versa. We also regulate the service here, so purposely hold trains there. For all these reasons, Edgware Rd, more often than not, will have trains idling on the platform or sitting at red signals waiting to come into a platform.
Any more questions?