Go with the biggest players to ensure the most successful outcome? Much has been said here already about the 'biggest players' and their ambitious marketing based on faded glory and past reputation - the suggestion that size equates to quality is not the case at all any more as budgets have been cut to the bone by successive owners whilst charges have increased and standards eroded; I was told that one of the mentioned no longer offers F2F pre-flight briefings, leading to instructors walking off the job in disgust.
What I would say in favour of integrated is that despite the cost, one important difference is that the entire process is managed, leaving the student to focus on training within an established timeframe. Modular demands a better understanding of the environment and frankly takes more effort and dedication unless you are lucky and find an ATO able to accommodate all of the modules (PPL to APS). Surprisingly, there are many integrated students who have absolutely no discernible drive to get through the course without spoon-feeding and little appreciation of what lies ahead or where they are going.
I am inclined to agree with B61's assertion that this thread is really an issue of confirmation bias as the OP is apparently planning to attend selection at CAE later in the year according to another thread. I recommend heeding the helpful suggestion of obtaining a Class 1 prior to parting with any money to an ATO, although I would also agree that the industry is due a downturn following perhaps the longest period of sustained growth and profitability in decades. I personally know a couple of former 'big school' graduates who have struggled to find flying jobs following completion of training in 2012 during the last downturn. Employers often require recent experience as well as currency, neither of which are easy to maintain when there are few jobs around.