I too was kind of confused the first time I hit the big city airspace trying to figure out which service. I'm led to believe that unless you are on a IFR flight plan giving you "positive control" your obligations and responsibilities under VFR rules remain regardless of what service you have Basic, Traffic or Deconflict. All the controller is doing when he advises that you're on a radar services is giving you a heads up that he's got you on radar but it doesn't mean much except if you were instructed to fly a certain route or height when requesting the transit they can verify you're complying otherwise you just fly your own navigation as requested preferably using VRP's as a reference till thru the zone you're transiting.
Again I'm no expert but as I understand it Basic service is good for RPS, weather info and giving rescue services a ballpark area of where they can find the wreckage and (up here in Scotland) the football scores if available.
Traffic services is as it sounds, if they have the time and equipment to cover your location to let you know about traffic they may do that but again are not under any obligation. And Deconfliction is basically if they see conflicting traffic they'll suggest a vector to hopefully avoid a mid air but again it's up to you as PIC not to hit anybody.
I could be wrong but that's my understanding.