Dave,
There were a number of occasions during groundschool and flying phase where I witnessed students with real competitive streaks! But then again competition is only natural if you consider the industry we are in...and I also think you will encounter competition whatever you decide to do.
I have a feeling that the course will have been much more competitive a year or two ago, but now the schools are placing many more students into jobs than they ever could before so theres much less reason for students to compete against each other. It's difficult for me to say whether integrated is more competitive than modular, as I have never experienced a modular course, but I wouldnt say it's a huge issue that should determine your decision as to which route to take. The biggest differences to consider are the intensity of the course and the dent to your bank account!!