How exactly are you copying? Are you sure the format of disc b is the same as disc a? DVDs should be UDF-formatted; make sure you're not doing a "data" copy to a different format.
The media, the burner, the write speed, etc., all play a role in compatibility with set-top players, too.
Again, the media (brand, type), the burner, and the speed at which you write the media make a difference. Older players also are sometimes finicky about recordable DVDs.
Also, the data rate of the DVD can cause stuttering; some players won't play high-data rate DVD-Rs, on some or all media brands. I find that keeping the overall data rate (audio, video, subtitles, etc) below 9.2 Mbps seems to be reliable on most players.
Well, if you're distributing videos, you need to be concerned about what your clients are playing them back on. This is mainly for final DVD distribution, especially of event video, etc... you want to make sure that you test on the most finicky players available, and make sure your products work.
A good brand of DVDs, such as Taiyo Yuden or Mitsui, will work on a much wider range of players than other brands.
If you know that your viewers will be tech-savvy and have recent equipment, then this isn't such a worry.
Well, there are labs that do testing of media quality/compatibility; these are the brands that always come out on top.
Taiyo Yuden and Mitsui are manufacturers of media. Every time you buy a particular Taiyo or Mitsui product, you know you're getting the same thing.
AFAIK, "Name" brands, like TDK and Verbatim, source their products from other suppliers. You don't really know what you're getting; they may switch suppliers at any time, and there are much more complicated quality-control issues involving multiple-sources.