For some reason my ride in to Greenwich from Swanley (so through Sidcup) is different to my ride back. In I come through Sidcup and follow the A211 up to Eltham, back roads from Eltham High St then past Eltham Station, A208/Shooters Hill, on to cycle paths alongside and above the A102 and then down in to Greenwich (this last bit is always the slowest). Pretty clear for traffic apart from a couple of sets of traffic lights but not flat considering it's approaching the river.
My ride home is Maze Hill by the park, A208 to Kidbrooke Park Road, A20 to where it almost kisses the A211 but there's no junction. Through the gap on to the A211 and straight ahead to Swanley. It's about 2 miles shorter but heaving with traffic and the Worlds of Leather roundabout is a pig to negotiate. Neither really have cycle lanes.
If I'm cycling in to the City from work I tend to cut through the foot tunnel and go along the north side of the river in. Even then the CS route can be quite busy so I'd imagine it's heaving of a morning. I don't do it very often though, and I'm yet to work out the best way to negotiate the Westferry roundabout. I've driven the A200 a few times heading to Borough after work and it's always been awash with bikes coming out of London but also very heavy with traffic. It doesn't look a bad route option if you don't mind traffic, but a couple of the junctions could be interesting. There's quite a lot of bus lane from memory.
Biggest question is do you have time to meander a bit, or is it a door to desk as quickly as possible commute?