Short answer is that the flat head bolt is the strongest solution, however the reasons why are more complex...
Everything else being equal (bolt material, size and hardness, tightening torque, bolt head size etc. ) it isn't the bolt that's the most limiting factor, it's more the material that the bolt is fastened through.
In general, the flat head bolt will be able to transfer more load into the material, because the force is transfered in one direction only (tension or compression, depending on the direction in which the force is acting).
With the countersunk bolt however, you have the force being transferred laterally into the material too, so the forces act to 'spread' the hole rather than try to pull directly through it. The material has already been deformed by the countersinking, so is already 'affected' and not in its ideal state. There is also less material below the head of the countersunk head than the flat head to resist the forces. So basically the countersunk bolt is more likely to pull through the material than the flat head bolt.
Leaving aside the material and looking at the bolt itself, how the head has been formed will also affect its strength. If, for example, the flat head bolt has been forged but the countersunk head has been turned (cut) the flat head bolt would again be stronger (everything else being equal) because the structure of the metal hasn't been 'broken'. This means the head of the forged bolt is less likely to shear from the shank. With a large bolt, it's likely that a countersunk head will have been turned but a flat head forged.
Then there's the fact that on balance, a flat head bolt head has more material to it than a countersunk head, so it's better placed within itself to transfer the forces into the shank than a countersunk bolt, which will tend to collapse.
As for the angle of a countersunk head, yes that makes a difference also. The shallower the angle (e.g. 60 degrees v 90 degrees) the more likely the head of the bolt is to 'collapse' in on itself and the material deform outwards and thence allow the bolt to pull through the material. The corect angle to select for a particular application is based on the relative hardness of the 2 materials (and other limiting factors like thickness of the material/allowable amount of protrusion etc.)
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