Interesting question, I would also like to know the answer to this. I don't think there is any harm in applying for several projects and different funding sources. You don't want to limit yourself or miss an opportunity, particularly in this economic gloom. Most academics/potential supervisors understand this, and would hopefully not take it personally.
Personally, I have only applied for one funding project in the EU under my chosen supervisor, and I am certain (knowing my field) that this is my best option. I am also re-applying for some research funding, I was offered some university funding to start off with, but that has run out completely. It really depends on the field that you are in and how well you network. It also depends where you apply as well, I have noticed differences in the UK vs EU funding.
Good luck with your funding proposals!!