Which of these two cases will have the most friction? I have a structure colored in blue which we are looking directly downwards on (birdsview). Its high up in the air, and the only thing keeping it from falling down is the friction surface (red) between structure (blue) and the steel plate (black line). The reason there is enough friction to keep the entire thing together is due to bolts (grey lines) pulling the whole thing together with a strong force, which creates friction.
What I am wondering is which of these two cases, given that the force pulling them together is equal, would see the highest friction force. Case 1 only has 2 friction surfaces, but the surfaces are larger. Case 2 has 4 friction surfaces, but the surfaces are much smaller. Since friction is F= N*μ the friction surfaces might not even matter and it only depends on the force pulling it all together?
Case 1

Case 2

 A: In both of these cases, the friction force is simply equal to $mg$.
Given that the coefficient of friction between the surfaces is the same for both cases, and the force exerted by the bolt is the same, the maximum possible force of static friction is also the same, by Amontons' Second Law, which states that the force of friction is independent of the apparent area of contact.
We're assume quite an idealized model - in practice, there might be some additional considerations to make, for instance, with the deformation of the structure under compression.
A: I the ideal case, there is, as you already hinted at, no difference between the two cases. A block of continuous material (with three different sides), resting upon a solid underground, will start to move when you apply the same minimum force to overcome the force of static friction.
The side you put the block on is of no importance. Each side needs the same applied force to start the motion. If set in motion, the static friction force will become the dynamic friction force, which is smaller initially, so the block will accelerate, until the force of dynamic friction becomes the same as the applied force. The block will not accelerate anymore and have a constant velocity.
That will happen if your construction is ideal. Normally, constructions are not ideal. If, for example, the walls with which you press (the black perpendicular lines in your pictures), are made of ice, the first picture can hold the steel construction, when the second can't. The pressure caused by the small surfaces, can alter the state of the ice that tries to keep the steel up. Like the pressure of ice-skates creates a thin film of water, which reduces static friction.
True ideal cases don't exist (due to the non-continuous nature of materials), but in practice, these cases come close, and materials can be considered ideal. Even the friction on ice can be viewed in this way, by taking both the liquid and solid state of water into consideration. In your case the situation looks pretty ideal, if the forces considered are not too large. If the system is linear, so to speak.
If the forces applied become very large, the response in the second picture might be different from the first. Just imagine the red surfaces get smaller and smaller. This will surely alter the friction coefficient, which in the ideal, continuous case won't happen. Besides turning liquid, the materials involved can alter each other mutually, thereby altering the coefficient.
