i ride 95% on public roads. I maintain that over the past 10 years ive been exclusively riding road bikes, bike trails are a million times more dangerous than the streets.
Runners, women walking with 1, 2, or 19 dogs...each one going in a different direction ready to close line you, women walking in groups gabbing away not paying attention, women walking and gabbing on their cell phone not paying attention, roller bladders, slow moving cyclists of all ages and kids not paying attention all act as potential hazards for cyclists on bike paths.
I've had to evasive action far more many times on the few paths i've ridden then the thousands of rides i've taken on a street.
That being said...if youre just starting out and don't feel comfortable with cars passing you 30 40 mph faster than your going, stick to the bike path.