Totally off the top of my head (and I'm open to correction) I understand that you'll derive these advantages from having a Permit to Fly as opposed to a C of A:
Cheaper maintenance. You can do more of it yourself.
No requirement to fit TSO'd parts.
Less restrictive regulatory regime.
Disadvantages:
No IMC flying.
No Night flying.
No hiring the aircraft out.
Permission required for international flights. (Note though that some regulatory authorities have issued a blanket approval for Permit aircraft to fly in their airspace. I understand at one time that the French were happy for homebuilt Permit aircraft to fly in their airspace, but they were not prepared to have professionally built aircraft, now operated on Permit, fly in France at all. I don't know if that remains the case. The PFA should be able to advise).
I can't think of anything else at the mo'.