I know lots of people who got employment relatively quickly via the modular route. I've seen people from integrated courses be passed over again and again and vice versa. Do not believe the marketing hype.
It is true that some airlines prefer integrated pilots, indeed integrated pilots from certain schools. But as it happens they cherry pick the best out of each class. But even then they still take modular pilots.
Really at the end of day it doesn't matter. There are few jobs at the moment. But when there are, it still won't matter. As clanger says it not about where you train but who you are.
I know one guy, modular trained in the USA. Applied on Monday, was called on Tuesday for an interview and assessment the following week. Passed and told on the day, he was in. Similarly, I know another from an integrated course, sent in the application and heard no more.
It really doesn't matter, get the best training you can for the finance you have. You'll need the spare cash anyway for the long wait for the job.