Rotor size does very little for stopping power on a road bike.

The reason you see 203s on tandems isn't for more stopping power, but for the heat dissipation. 203s offer a much greater surface for heat dissipation. 160s will stop a tandem just fine, but 203s will stop it repeatedly better because the pads and rotor stay cooler. This is especially important on tandems in hilly or mountainous regions.

I have 160s on my road bike and the only time in 18,000 miles that I ever needed a bigger rotor was on a 14-mile descent in the Rocky Mountains, where I was riding the brake for the better part of 45 minutes.