There is no direct reason to WHY the Turbo Powers are stronger/more powerful then the Zeo powers. In fact, this little change up in powers is often a sore point for many fans, since there's no reason to replace the old Powers if they're still there, are capable of getting stronger (since it was said early on in Zeo that the Zeo powers would keep getting stronger, like a perpetual power source) and nothing had happened to the old Zords and powers.
This is, of course, if you ignore the Hoax of 'Scorpion Rain' where supposedly several of the Zeo zords (and possibly powers) were destroyed in a fight with Serpentera.
Regardless, Power Rangers is a show that relies on footage from it's Japanese counterpart, Super Sentai, and thus when Power Rangers wanted to move onto it's next season, they needed to use the new footage. The creators, however, never gave us a proper storyline on why we had to use the Turbo powers other then 'They will help you get into the magic island where the bad guys of the movie are.'