I believe this means the quality of the faith given to all believers is the same. The quantity (or depth) is not. I think Remas is correct that persecution is a factor in growing faith. But I think persecution acts more as the agent of growth than the means to growth. Without persecution as a motivator, material comforts certainly will dissuade many of us from stepping outside our comfort zones and risking what we have. So without persecution, what then becomes the agent of growth? Jesus' call.
Dietrich Bonhoeffer, in his book "The Cost of Discipleship", links faith with obedience. He wrote, "Obedience remains separated from faith. From the point of view of justification it is necessary thus to separate them, but we must never lose sight of their essential unity. For faith is only real when there is obedience, never without it, and faith only becomes faith in the act of obedience."
Therefore, our faith will grow and deepen only insofar as we are obedient to Jesus' call. Peter was obedient to the point of death. The depth of his faith must have been great. This is not to say we should strive for a martyr's death so that we can have great faith. Following our own calling will never grow our faith. Only by following Jesus can this happen. Whatever Jesus calls us to, if we are obedient then our faith will grow.