For airline work - contact lenses wouldn't work for most people (I suspect) due to the dryer air in the pressurised hulls causing them to dry out pretty quickly and become uncomfortable. You'd need to be constantly blinking to keep them moist. It is the advice to passengers so I presume it will be the same upfront! However, you don't have this issue in a typical GA plane...
See
Guidance on Using Contact Lenses by Pilots | Medical | Personal Licences and Training for official (and surprisingly comprehensive) advice.
I wear prescription glasses / sunglasses in a plane but have tried contact lenses on the ground in the past. I've tried monthly ones and daily ones but the job I do (staring at a computer screen all day) meant that my eyes were stinging at the end of the day's work, so they just didn't work for me. They also had a habit of coming out at the most inopportune moments...
Also - it depends on whether you have slight astigmatism as well as distance correction (many people do without realising it). Glasses tend to correct this as well without you realising it while contact lenses don't. I found that I could see with a slightly better clarity with clean
lenses than I could with contacts.
One other thing - no one likes the idea of putting things in their eyes but you soon get used to it - its not as bad as you think it is! There are a couple of different techniques so if you go for them - don't be afraid to try and find what works for you. I found a different technique to the one I was "taught" in the shop was quicker and easier for me - but everyone is different.