A bagua mirror combines the feng shui power of a mirror with the power of the feng shui bagua. Mirrors are called the aspirin of feng shui for a reason, and bagua is a very powerful symbol with complex layers of energy and information.
Let me start by first confirming some basics. First, the feng shui bagua mirror is always used outside your home, and never inside the home. Second, it is best to use the feng shui bagua mirror only when recommended by a professional feng shui consultant; chances are, the bagua mirror is not necessary for your front door.
As for the difference between the feng shui bagua convex mirror and the feng shui bagua concave mirror, the following info should be helpful.
Concave Bagua Mirror
A concave bagua mirror is used in the feng shui applications when the negative energy outside needs to be neutralized by being absorbed. Basically, a concave design of a mirror will "suck in" the negative feng shui energy and neutralize it. While this sounds easy, you have to know how to distinguish between negative energy that can be absorbed by a mirror versus knowing when to create a protective shield around your house.
Convex Bagua Mirror
A convex bagua mirror is used when you want to reflect back the negative feng shui energy (Sha Chi) pointing at your home (be it front door or any windows). This is the least desired feng shui use of a bagua mirror because it just promotes the endless bouncing of negative energy. Sometimes people do that when they have negative energy coming from their neighbors' house, but I assure you a convex bagua mirror will not help alleviate this situation.
There are smarter ways to deal with incoming negative energy by creating purposeful protective energy with your landscaping, with specific garden design features, as well as the outer design of your doors and windows.
There are many subtle feng shui ways to redirect the negative energy from your front door and strengthen your house with more protection.
In the Western feng shui applications, I have rarely seen (or recommended) a feng shui bagua mirror, be it a concave or a convex one.
More often than not, a feng shui bagua mirror will look completely out of place on a modern house, as well as be there for wrong reasons.