I think our differing views probably boil down to personal preferences re train vs tube. Tubes don't provide better transport than trains; they just offer slightly different positives and negatives. It depends what you value/prioritise when travelling (like space, light, access, frequency, safety).
I don't think buying near a tube line necessarily brings better transport connections. If you're close to multiple tube stations on different lines and therefore have options when there's a strike/breakdown/trespasser/unexplained cancellation and delays on the tracks etc that will give you better connections than being near only one station. But having a few different train lines (and East Dulwich also has Denmark Hill - close to your first property link - a 5min bus ride away, as well as Forest Hill in the other direction, giving plenty of options if one line happens to be closed) gives you the same options and more comfortable travel. I don't consider a 7-10min train ride from central London to your home station in a nice area arduous travel, but if I could spend £3million on a property without blinking an eye, I'd hire a private chauffeur.
The second property you linked to is in Stockwell, which is the only one that is relatively close to 2 tubes. I wouldn't say that was close to Vauxhall bus station. Not a million miles, but not next door. I guess it depends on your stamina and attitude to risk, but I also wouldn't choose to be walking all the way there after a night out in town. (I wouldn't see the Northerline as a positive link either, given it's more crowded and has the worst crime rate than any other line.)