The problem here is the media - sort of - because it really doesn't have anything to do with the media manufacturer. It is completely Sony's fault. The 510a is a 4x maximum drive, and Sony hasn't put out a firmware update for the 510a dvd burner since 4x media days. I could not even get reliable burns from this drive using 8x media, never mind 16x. I complained to Sony ad nauseum about this, but to no avail. So, I bought a new drive - and it surely wasn't a Sony! My Sony 510a is in pristine condition - sitting in a box. My Benq drives work great and burn anything I throw at them. I still recommend Benq dw1650's to folks - if you can find them somewhere.
The 510a is the last dvd burner actually made by Sony (they just slap their name on someone else's burners these days - for more money, of course), so I don't think there is even any chance of cross-flashing it to an oem manufacturer to apply updated firmware.
Your laptop drive is also apparently a 4x burner (a Dell laptop, I expect?), so I expect you have the same media incompatibility problem with it. I've read somewhere that it is actually a Lite-On drive, so maybe some newer firmware is available that supports newer media types and speeds. You'll have to search around or contact Dell for help maybe. Good luck.