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Flight Connections isn't just for those with connections on one ticket, you can use it to start a new trip there if arriving from another service and without checked bags. If you have a passport from one of the e-gate countries then it's generally quicker to go out to landside via the UK Border instead of Flight Connections, particularly if you have either Fast Track or the First Wing access, and particularly before about 16:00 hrs. Thereafter it's probably much of a muchness.
If your next flight is less than an hour away, for multiple reasons you best used Flight Connection, even though it may take longer.