Don't worry about the winch brake being inside the drum, this is only going to matter if you 'power out' the rope with you truck hanging on the other end (lower down a slope for instance).
Synthetic rope has a number of disadvantages against wire rope, it is more easily damaged and it does need replacing more frequently. However, a synthetic rope doesn't stretch very much and so doesn't store any energy so when/if it does break it doesn't whip about like a wire rope and in fact 98% of the time drops to the ground. Synthetic rope is also lighter and easier to work with and doesn't ever have finger shredding wire fragments sticking out of the side.
In short then, yes synthetic rope is always my choice and is worth the money for piece of mind.