Again, gotta say that you should check your commute. I also live along the national rail and tube and depending on my route, I choose different trains. If I wanna get to London Bridge in six minutes, I take the overground, if I need to get to NW london, I take the tube.
Just to add, though the overground is great, it can be a pain in the ass. Often, there are delays at the platform, the trains often run slow depending how many trains are ahead of you, and I find that trains aren't as frequent as tube. Tube there's usually a train going the route every couple of minutes (if it's running well), overground is usually at least ten to twenty minutes (if it's running well). Last winter when there was a lot of snow, my overground route into London was shut down, so I took a bus and went to the tube station, which ran the Jubilee line.