I would check for any known delays to services before deciding which Underground line to take. The 'tube' (Bakerloo/Victoria) option will probably be a few minutes quicker than the 'surface' (Circle/District), but by taking the Circle you could avoid the need to change. Particularly if you've got heavy/large luggage with you, the slight larger surface trains may be more comfortable and will certainly avoid the need to negotiate escalators.
Southern Trains definitely a better deal than the Gatwick Express, but at least with the Express you can be sure you're on the right train! If only there were similar competition for the Heathrow Express - don't be tempted to take the Piccadilly line 'tube' from Heathrow unless you've got a lot of time to spare ...