You've already said it. The airlines are pretty much all after the same thing in their prospective (pilot) employees. Think about the qualities that you would want in a pilot if you were employing; good communication skills, a strong sense of responsibility, leadership experience etc etc etc. The list is very long! All you have to do on a CV is give them the flying qualifications that make you employable (as I listed in a previous post) and some desirable experience.
If you have management experience in a previous job, or have had responsibility in a safety critical environment, then this is desirable and worth mentioning in your career history. BUT, don't forget that the CV is a taster to get them interested enough to call you for selection, so don't harp on and on about the number of people you managed and the 'responsibilities' (read job description) endlessly. You can expand on the 'simple' facts at interview if asked, the CV is NOT the place to get life histories down.
If you keep is simple AND relevant you will keep their attention and their 'first scan' may be enough to get you into the 'further, closer inspection' pile. Consider a poorly presented CV sitting next to a professional looking one, could even be the same candidate! Which one do you think would naturally be more appealing? Obviously the one where they can see clearly that the individual meets their minimum requirements and has some desirable experience (be that aviation related or non-aviation). If the same candidate had another CV that looked bad, was poorly laid out, with the required detail either hard to find or missing, with waffle about 'communication skills at all levels' when talking about their part-time job in McDonalds.......well, it doesn't take the brains of an Archbishop to work out which candidate looks the better on paper.
Remember that last point too. They are looking at you on paper to see if you fit the bill, just like an application form or CV for ANY job. It is important to sell yourself on paper, which is different from how you are going to sell yourself face-to-face in an interview. If you are great at interviews you are selling yourself short if you miss out on interviews because your CV is so poor.
I see many Wannabe CVs and the quality varies significantly from absolutely abysmal to pretty good. A good CV is NOT going to get you a job on its own, but the whole recruitment process into airlines (from the candidates viewpoint) is about minimising the risk of failure through dotting 'I's and crossing 'T's. The best candidate may not get the job; the best presented candidate will usually be the one who gets the job offer. So a well presented CV and cover letter, or good application form, good interview technique, well dressed and presented individual with a well polished sim performance is the more likely successful applicant.
Minimise your risk of failure at each stage through good preparation, research and CONTROL.
PP