The ending theme is called "Never Dream", so I thought it obvious that it was meant as BAD END...but while using Google to be sure I had the music's name right, it's possible I've been wrong all these years. There's an official "Phantasy Star Compendium" in Japan and, if the translations are to be believed, it states that the heroes defeated the "Earthmen race" but what happened afterwards is unknown. It's possible they all died anyway, but they did kill all humans first.
http://www.pscave.com/other/compendium/ (Translation of the compendium. Spoilers for all four Phantasy Star games, obviously)
http://www.pscave.com/other/compendium/page61-65.shtml (the relevant section, which also has spoilers for everything. It's a timeline of the series, look at 1284 for 2's events).
Yes, to find out the truth about the ending you had to get a Japanese only Compendium and you're still left with the absolute final answer being unknown.
--
In this world which will someday fall to ruin...
...dreams and hopes don't matter at all.