I have timed this. The airside connection is faster than the landside connection by quite a margin. Also North security via Flight Connection is faster than exiting and re-entry, even first thing on a Monday morning.

The airside bus takes 12 minutes on average, the service frequency is 8 minutes, so 16 minutes terminal to terminal. HEX takes 4 minutes, but a service frequency of 15 minutes. You also need to add in quite a schlep down to and back from the station, particularly at T3. Airside gate to gate is well under an hour (52 minutes), landside gate to gate is over an hour, though for T1 domestic it is probably 50/50, due to the layout.

My longest ever wait time at T5 North security is 17 minutes, my current average is 6 minutes and that is with a sample of 72 since Jan 2011.