Not sure about now but when I used to live in the Peckham/Camberwell area, it was standing room only from Peckham Rye in the mornings. Evenings and again, most (including myself) got off at Rye, all piling down into that nasty stairwell often made even more fun when the arrival of a London Bridge train co-incided with a Victoria/Blackfriars service.
Think some posters who were inferring that the bus is usually the better option seem to forget areas such as Old Kent Road, Camberwell Green and Elephant & Castle, all absolute nightmares when trying to get in from South London to Central by road.
A lot has changed over recent years to affect the dynamics of these services, but there is a fundamental issue of slowness which affects a number of the Southern lines. I live equidistant between West Dulwich and West Norwood stations, but the journey times to Victoria are 13 and 23 minutes respectively, so you'd always go to WDU. I'd say on the trains from West Norwood more alight at Clapham Junction than Victoria. From areas like Streatham there are incredibly frequent and reasonably quick buses connecting with the Victoria Line at Brixton, which is a very fast tube line, and also more likely to take people where they want to go than a train which terminates at Victoria.
Demographic change has played a part. The line via Peckham Rye was always a bit of a backwater but then previously unfashionable areas like East Dulwich became popular with young professionals who commute to the City, and I imagine peak hour usage of that station must have shot up since the 2000s, in normal times morning high peak trains are very busy leaving that station.
The other factor is the Overground, which means a lot of passengers pile out at Peckham Rye and change, the connections off Southern into Overground towards Canada Water work well. This trend has been even more marked on the Forest Hill line, where the extension of the platforms to 10 car coincided with the arrival of the Overground, which has turned out to be much more popular not just with Canary Wharf commuters but also people travelling to the west end for the easier (although very busy) Jubilee Line interchange there. So that means that 10 car Southern trains to London Bridge are quite lightly loaded, especially towards the rear, while the 5 car Overground trains are rammed.