hi jim, welcome to pprune!
I don't know what gave you the impression that OAT, BAe, Cabair etc. fail slightly in the flying side of things. They are all reputable, approved schools with high quality training. There are also lesser well-known schools in this country that provide training to the same standard but for less money. BAe, OAT and Cabair are the only three schools that are approved by the CAA to run Integrated full-time courses, hence why the airlines use them. They do have very good names, but don't get too hung up on the reputation of schools, recent GAPAN research suggests that the airlines aren't all that bothered where you train. Use your head and do plenty of research on Pprune and you'll make the 'which school' easily enough.
As for Intergrated Vs Modular, now you've opened a can of worms! Before the Lynching begins, I'd suggest you do a search of Wannabes on the exact words 'integrated vs modular'. You will get a serious number of hits with that baby let me tell you! It has been done to death here in the past
hope that helps!