You have to remember that all agencies are governed by the Recreational Scuba Training Council (
WRSTC :: World Recreational Scuba Training Council) that sets the minimum guidelines that all Scuba Training Agencies have to follow.
The agencies then set clear structure for the Instructors who operate under there organizations umbrella.
Sometimes these Instructors are money grabbers and will sign your C Card even if you can only marginally accomplish the prerequisite skills.
Some will not give you a C Card until you have a level of competence which satisfies not only the instructor but goes above and beyond the standards.
Safety factors are relative.
If you have a crap instructor, you will most likely be a crap diver as you have not had the training required to do this safely.
Find a good instructor, one who works closely with you and will mentor you in areas of concern and will provide critique and actually gives a damn about you coming back safe, regardless of agency you will be a safer diver.
Bottom line is interview Dive Instructors and get a feel for them.
There is a thread on Scubaboard that has some of the questions to ask when interviewing a trainer.
That said once certified OW, safety is all down to you. Once you have your C Card you can do what you want in open water to a limit of 60 to 80 ft, depending on agency.
Dive to your comfort level, don't push it, and never be afraid to scrub a dive if you feel something is not right.
All of the above said look up Doing It Right.
Global Underwater Explorers (GUE) and Unified Team Diving (UTD) are more expensive training agencies yet worth it. Talk to them if you want to know why.
I will be doing Fundies or Essentials in 2014 to get a better grasp on my diving even though I am certified.
Happy Diving and good luck.