Beta quadrant comprises Old Earth and many human-settled colony style planets. (Staff Sergeant Wodin Whatthehel, for example comes from a nordic-cultured planet in Beta Quadrant). Although there are many asteroids and planets that are resource based in this quadrant, it is largely concerned with trade, agriculture and textile goods.
The GAF does most of its training of raw recruits and officers in quadrant on NonCom and Officer Planeta, terraformed worlds created by the GAGA to organize, train and polish its soldiers.
The Gamma quadrant is foremost in primary resources, especially mining. Most of the habitable planets in the quadrant were terraformed to one degree or other to make them suitable for human life.