I make a lot of T4 to T3 connections and, unless you're a real laid back person, you're asking for agita. My eastbound concorde experiences have been of frequent, usually short delays. So to start with, you're thin margin for error is in jeopardy. It is true, that CX will, if they're willing, be able to meet you at the gate and give you an airside transfer to the Connections Center at T3. This could save you 25 minutes vs. walking to the connecting bus station and waiting for the bus.You then have to go through security at T3, which as other posters have said, can be relatively quick or not so quick. I've twice missed connections (once necessitating an overnight) when taking the Concorde.