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Bottom Line - (IMHO)String:Trying to be careful here but basically.
PADI:- Learn to dive/advance quickly with courses taking typically a few days
BSAC:- Takes a lot longer, up to several months per course. You may well finish the course with a lot of experience and dives though (more than the required minimum). Example i qualified it took months but i had 20 dives (as opposed to the minimum 5).
Reason for this is PADI is a commercial entity whereas BSAC is mainly club based with members typically meeting once a week for a club night and diving on weekends only. Instructors dont get paid so all training is voluntary.
PADI:- Pay for every course
BSAC:- Courses are free, you need to be a member of BSAC (~£45 a year) and a club but once thats done training is done free. BSAC does have a few "schools" where courses are sold in the padi way but these are few and far between.
PADI:- Standardised training and standards for everywhere in the world
BSAC:- Standards are catered more towards UK (or local to the area) diving and some things in a lot more detail in some areas as a result
PADI:- Clubs are rare and most are attached to dive shops. Most diving is done via dive shops
BSAC:- Diving normally done in clubs who own and operate their own boats so it works out quite a lot cheaper than using dive shops. Everything is run "at cost" only for legal reasons so the charges just cover insurance and fuel etc.
Although there are syllabus differences in training there are pros and cons to each agencies. I can think of thinks i like and dislike between the two but definately not going into detail here or it'll start a 30 page riot.
Note:- Both agencies qualifications are equally valid anywhere on the planet and you can join a bsac club with only padi qualifictions and so on. It isnt a rigid divide once you decide what to do with which agency. For example i started out BSAC, did some TDI qualifications and then did PADI. So im now qualified by 3 agencies (PADI OWSI and BSAC OWI cheque is in the post...).
Tried to keep that fair. Its my personal view of how things are between the two of them.