There is not now, and never has been, any independent evidence that self-sponsored integrated training improves the chances of employment. It used to be true that more integrated students than modular gained employment within a year of receiving their licence but this was when a significant number of employers sponsored training, which was invariably integrated.
OATS (as it then was), for example, used to claim that 90% of its integrated students were employed within a year of completing the course but, considering that all of those students were either wholly sponsored by BA or part sponsored by BM, such an employment rate was hardly surprising. You will find it very difficult to obtain equivalent figures for only self-sponsored integrated training as the results would not be as favourable to the schools' marketing efforts. Oxford is chosen only as an example, similarly misleading advertising techniques have been and are used by all of the integrated training providers.