as with most things in life, is not that simple. firstly how do you define a race? if you remove the driver (due to the number of variables it introduces) you can compare acceleration, topspeed & cornering ability as the 3 main characteristics which will affect race performance. drag will also be a minor factor in a top speed race, but due to the minor influence on low speed shopping cars will discount the drag variable.
power itself is a useless comparison, it does not consider weight. comparing the power to weight ratios will be a much better comparison. even more useful would be the torque to weight ratios. i think if you considered this you would find the peugeot actually appears to be the better car.
next stage of analysis considers the efficiency of the power and torque curves for both cars. at what rpm does max torque delivery occur, over what percentage of the rev range does 90%+ of the torque actually get delivered? what is the maximum rpm of both engines?
next consideration is the gearbox ratios. a shorter gear will be easier to turn, but it will also require an earlier change. for a drag race that considers acceleration up to 60mph, the shorer geared car will most probably have an advantage, assuming identical engines.
the vast number of vaiables makes it impossible to say which car will "win a race". you must define what a "race" is, identify the vaiables that influence race performance, calculate these variables, create a formula that allows the variables to indicate race performance as a numeric value, then compare the values. this could be a very difficult thing to do, and would be a good study for a final year uni project. creating a mathematical expression of a cars race ability is very difficult. i have only mentioned less than 10% of the things that influence a cars race ability.
at the begining of this post i mentioned the removal of the driver from the equation, this was done because the cars are so similar that i think the biggest contribution to race performance will be driver ability. the best driver would win in both cars.
if you forced me to choose a car i'd take the 206, it has a stiffer chassis, better wheel base width to wheel base length ratio, the gears feel shorter and the engine is revvy, its also lighter than a brava. however if you said a bravo or 206 i'd be stuck to choose, they are so similar it makes bugger all difference, as long as im driving id win