Better for What?
Which school is better? This is a query which has been keeping us awake at night since the concept of "teaching" was first concocted. The answer is obviously: there is no point is asking yourself, or others, which is the best school, without first deciding the criteria on which to base such a qualitative and, more importantly, subjective judgement. The word "best" per se has no meaning.
Teaching and Training Styles
The only criteria that really matters in my opinion is the teaching method. After all, an effective teaching method that suits one's forma mentis and abilities is paramount for effective learning. When it comes to diving schools, the teaching method is intrinsically linked with the target demographics. So the question then becomes: what are you looking to get out of diving? Is this going to be a one-off experience? Do you just want to give it a try? Are you doing this purely for seasonal leisure, i.e. something once every so often when you are by the seaside? Or do you plan on making diving your primary hobby?
Turns out diving is such a complex, and somewhat unnatural activity, that there's probably no way of knowing before trying. You might argue that this is true for most unknown things in life. However underwater breathing is something that humans aren't meant to do, and thus diving carries an inherent psychological stress, which is unique to it. There is no way to know how you will react to the regulated breathing, the water above you, the abyss below you, the depth, the potential claustrophobia, before trying.
Why do I mention the demographics? In my opinion the objective of PADI has always been to get as many people as possible to scuba dive for fun. This is achieved by initiating divers with (very) short Open Water courses which, upon completion, allow you to dive up to a depth of 18m accompanied by a Divemaster or higher. Short means that it is not uncommon to knock out the full course, including theory, confined and open water practice, in three days during a week long stay in a holiday camp. This raises the question on how much understanding, and mastery, one might gain in such a short time. Then again, the PADI Open Water is aimed at the aforementioned seasonal leisure divers, which will most probably always dive with clubs in tourist villages, on simple fish-watching shallow dives. Nothing wrong with that.
Other diving schools and federations, on the other hand, target enthusiasts who wish to learn diving to gain competence over the discipline. These are people who might think of turning diving into their main year-round hobby. BSAC is an example of such a school. CMAS is another. The former is the main British scuba association. The latter is a confederation of local diving schools across the world, which abide by the same regulations and teaching syllabi. The objective of these schools is in my opinion to form qualified competent divers, rather than to get everyone in the water as fast as possible. For completeness sake, I am a CMAS 3* diver and BSAC Assistant Instructor. I have also tried the PADI system indirectly by assisting during an Advanced course. So yes I speak from personal experience and might indeed be biased.
Having said this, you will most probably find the syllabi of the various Open Water comparable courses across different schools, as well as the mutual equivalences and recognition between them. These should already give you an indication of the amount of learning and dedication required to complete the course. This in turn is representative of the quality of the courses, in terms of competence levels and goals. I remember learning the mechanics and physics inside the workings of a regulator during my CMAS 1* (first level) course. I do not recall reading about it on the PADI Open Water manual. Whether this knowledge is useful to a first level diver is all up to you -- the student -- and it depends on where your interest in diving comes from.
The BSAC page on crossing-over mentions the equivalence between PADI and BSAC certifications:
For example – divers transferring from PADI:
PADI Open Water or Advanced Open Water
Similar to: BSAC Ocean Diver
Progress to: BSAC Sports Diver
PADI Rescue Diver
Similar to: Sports Diver
Progress to: Dive Leader
Here is the full document in PDF.
This page has a more comprehensive breakdown of equivalences between diving agencies. Remember to contact your club for more precise information.
My Personal Opinion
Finally, any answer to this question will carry a heavy opinion-based component. So here is mine. I have trained in Italy and France with CMAS. All my CMAS instructors made me feel safe. They were competent and looked like they were in control of everything. And that's the most important thing in my opinion when doing something potentially life-threatening. I found BSAC a bit too pedantic in their breaking-everything-into-baby-steps philosophy. Then again they often deal with people who are not comfortable with swimming, let alone diving, so this method might be the most effective. PADI's first level courses -- Open Water and Advanced -- always gave me the impression of being geared towards making a profit, rather than forming competent divers. Their semi professional courses -- Rescue and Divemaster -- are somewhat different in this sense.