First of all you will need an architect to design whatever it is you are doing, and then you will need to get a permit. Then you can get bids from contractors. At the end of the day, I imagine concrete will be harder & more expensive as well.
Good luck to you, Jirius Isaac
Since a 'mezzanine' is a mid-level, between two floors, I presume a concrete mid-level would be more challenging and more costly to design, to frame, to support, and to pour? When compared to a wood-framed mezzanine, I expect concrete would be more expensive. However, there are not enough details to enable anyone to provide you with an informed answer.
There are so many questions to be answered here -- I think you would do best by getting a consultation with and quotes from specialists in both fields. Remember that price is not be the only factor and may not be the most important one. You will want to consider appearance and functionality, and will want to see examples of each in place with similar usage if at all possible.