Both students come out with generally the same qualifications. A modular student could just as easily find a job before an intergrated student and im sure even before an intergrated student because as said before they may have made their 'face known', networked hard etc etc. On the other hand an intergrated student could just aswell find a job before a modular through say a recomendation etc. Its true BA will only take intergrated pilots from approved schools, cabair, oat, fte, but doesnt mean just because the national carrier doesnt (take modulars) others wont, flybe will happily take modular students but i quote this after asking the question to recuirment at flybe "intergrated students have that edge" dont ask me why or hes wrong, im just saying thats what he said.
People choose intergrated or modular on their own accord, whatever they choose good luck to them, and no one is going to hand anyone that first break, it comes through hard work and perseverance.
*all of this is in respect to the first job, BA would happily take any one who has enough experience.