There is no quality difference between different DVD regions. The apparent reason for the regioning, to me, is that media companies have some shit about not wanting people to be able to view and, more importantly, sell DVDs in other regions, as well as for anti-piracy. Think about it this way:
If "Movie X" were really big here in the US and Japan, but got released on DVD here in the US first, some enterprising person in the US could sell the DVDs mail order or directly in Japan, without giving the movie companies any money beyond the initial DVD purchases. With regioning the movie companies can control the release and sales of DVDs.
As for piracy, Hong Kong, for instance, is region 6, I believe. The US is region 1. The idea is that a region 1 disc will not play in a region 6 player, and vice versa, so there is less of a chance that some HK pirate will rip, copy, and undersell the movie companies. Of course, it hasn't panned out that way, so regioning has become more of an annoyance, if anything. There are, as Misty mentioned, region free players, and most computer DVD drives seem to be region free also.
<a href="http://hometheaterinfo.com/dvd3.htm">DVD region list</a>.