Integrated vs Modular makes little difference from what I've seen. Perhaps for easy & ryan it does?!?
My experience while working for a UK airline over the last 2 years was quite an eye opener. The Recruitment Captain would do an admin day in the office once every ten days. His way of sifting through the mountain of CVs was to take the top half and drop them in the bin! The bottom half was then reduced by removing everybody over 40yrs. He then removed any that couldn't write a properly constructed covering letter. Anything over 2 pages was binned also.
Having spoken to numerous people who flew with the company it seemed a combination of things provides the winning formula. Hours, personality, team players and also being prepared to go beyond the minimum required. I know of some integrated Oxford students who got rejected two or three times.