Can you apply to both the cargo and pax side at the same time? I'm assuming you can..can I use the same resume, cover letter etc..?
No. On the application form you are asked if you're applying for AJX OR AJV.
Are they like the US majors with 10,000 resumes on file?
Nobody will know the whole answer to this question as applications go through agencies, not direct to the Company. With Parc, CReW and IAC all involved, who knows how many people are applying. More to the point, though, why does it matter? If you are qualified and want the job, then apply. As I've said before, the worst thing they can say is 'no' and you have no influence whatsoever on who else is applying, so don't waste brain cells worrying about it.