Some people just don't agree with the way integrated courses are structured.
I personally think that aside from a couple of cases, MOST integrated courses are going to leave you in the same position job-wise as modular, with the same licence but maybe 2-3x more in debt/in expenses and less hours to show for it!
I am far far from the most experienced person on here, and am actually relatively new in the industry, but I spent a lot of time making contacts before/during/after my training, and I haven't spoken to any HR/recruitment in any airline (including legacy, regional jet and tprop stuff) that gives a stuff about where an EXPERIENCED pilot has trained. It can be different for the new guy with no experience and only a flight school record to show for himself but even then, apart from the airlines that have schemes with certain (integrated) FTOs most of them don't seem to differentiate between modular and integrated, at very most they seem to ask for one stop modular.
I don't think it can be compared to public/private schools, because as is often proven by league tables and the like, and also through general rumour and word of mouth, private schools are often deemed to provide a superior education to other schools. this does NOT translate into the modular/integrated debate (were most of the integrated superiority talk comes from the integrated FTOs themselves) because I have not seen much evidence which proves an integrated graduate to have superior training to a modular one, and in fact I have personally heard of some airlines (mostly smaller ones to be fair) preferring modular students due to what the perceive as a more rounded pilot with broader experience and some determination and wit about them.