How to properly ventilate a Mansard Roof?

I recently purchased a home with a Mansard roof, I had some roofers come to give quotes to replace the top (it is finished) and they all recommend adding ventilation (known issue with Mansard's).


The problem is that they are offering two different solutions and I don't know which is best... hoping for some professional recommendations from the community.

1- Maximum Mansard Air-Intake drip edge
http://www.ventilation-maximum.com/English/product-air-intake-soffits.html#mansard
This is what 95% of the mansard homes on my street have and is the more expensive option

2- Ventilation Maximum (VMAXAT1 or VMAXAT2) uniformly positioned at the eaves
http://www.ventilation-maximum.com/English/pdf/product_special-air-openings.pdf
There is 1 house on my street that has it and it is less expensive


Any advice, first-hand experience, or help for me to decide which would be the right solution would be very much appreciated.
Thanks,

Seems like my terminology might have been bad - when I say "finished" I mean it needs to be replaced immediately - the previous owner block all the soffits (thought they were mistakes) - so now I need to tear it down - while I am doing that I am going to improve the ventilation and thus my questions.

The roof is NOT flat (small pitch, not sure how many degrees), and there is an attic that I can get to and almost stand-up in (so pretty large).

Right now the roof top is the same as the sides, shingles (falling apart), and I plan to put new IKO 50 year fiberglass shingles on - would have loved metal but can't afford it.