Car A has higher power, but car B has higher torque. Which one would win in a straight drag race? Suppose we have 2 cars with different specifications.
Car A has a higher power specification but  a lower torque specification.
Car B has a higher torque specification but  a lower power specification.
Suppose they enter a drag race on a flat, straight track. Who will win the race?
 A: Car A will win, if it has the right final drive ratio. Power is (torque x RPM) so an engine with high power but low torque develops its power at high RPM. Once you gear it down appropriately, it will win the race.
A: The single power or torque number does not tell the whole story.
You need to know the power band of each engine which is a graph that tells you the power/torque provided at each value of rpm.

The higher powered car can still  fall behind the lower powered car if the lower powered car is able to provide its power/torque across a wider range of rpms.
A: 
Who will win the race ?

It depends.
Depending on the other specifications, namely

*

*the exact torque/power curves and

*the geartrain ratios of each car,

you could have car A win or car B win.
First of all, just to get something out of the way, because this question seems to be intended to ask, "which is better higher power or higher torque?". That question does not make a lot of sense, because the power and torque of a car engine are not independent of each other. Both have a strict relation between them. Given the power curve of any engine, you can calculate its torque curve and vice versa.
The peak power/torque is less important than power/torque CURVE
Regarding the specific example you have asked about, one thing to understand is that the specified power and torque of an engine are generally the peak power and peak torque. The engine, in general would not produce that power or that torque throughout its operating rpm range. So, the cars would neither produce the same power, or the same torque from start of race to end of race.
What is more important is the power/torque CURVE, which tells us the torque/power produced by the engine at each value of rpm, rather than peak torque/power. One car may have a higher peak value, but that peak value could be concentrated only at a specific rpm, while the other car might have a lower peak value but it could be across a broader rpm range, so that, at most of the rpm range, it would have higher value than the other car, even though it's peak value might be lower.
As can be seen by the diagram i am borrowing from Knight watch's answer

The red car engine has higher peak power, but the blue car engine has higher power in the rpm range of 0-5000.
Similarly, when it comes to torque, the blue car engine has higher peak torque, but the red car engine has higher torque in the rpm range of 5000 and above.
This diagram is just an example, and the car with higher peak value might still be faster . But, in general, only the peak value does not tell the whole story, without knowing the value over a range of rpms.
So, the specification of peak power/torque is not the only thing which would determine the winner. Power/torque over a range of rpm also matters.
The role of the gearbox
The other important deciding factor would be the gear ratios used. These will determine which car will be better able to stay at its peak operating rpm for most of the race.
Race distance matters as well
One more factor that would matter is the length of the race. A shorter race could favor one car, whereas the other car could win in a longer race.
So to summarize, just comparing peak power or peak torque would not give an answer as to who will win.
To get the answer, you need to know

*

*the power/torque curve of each car

*the gear ratios of each car

*the distance of the track from start to finish
(assuming of course that other things like weight of car etc. are equal).

A: Torque is a fetish for solving the transmission non-idealities.
The power wins the race. But it is not the maximal power of the engine, it is the average power output of the engine for a given type of competition.
One can easilly find a truck or even a tractor with a mind-boggling (from a racng cart viewpoint) engine torque and a medicore (from a racing car viewpoint) engine power. A race between a car and a truck is usually pointless. Tractors are not better.
If one dives into the math of the acceleration, one will find that the acceleration is proportional to the torque at the wheels. This is not the same as the torque at the engine flywheel.
There is a transmission in between.
And if one assumes that the transmission is loseless (or has a constant efficiency which is almost true) it boils down to maximizing the engine power.
And now we find that the engine is not that simple. It has its maximal power at some rpm and less at both higher and lower rpm. The driver has to switch gears in order to keep the engine near its maximum power rpm.
The gearbox may have its gear ratios widely spaced and the driver will switch gears less frequently, leaving the engine more time away from its maximum. On the other hand, the time needed for switching gears will be less (and the time used for switching gears is lost for the acceleration).
And here, a high-torque engine may help. Somewhat.
High maximal torque is a "proxy" for a wide power peak at power vs rpm graph. It is not a good criteria, as any atmospheric diesel engine will tell you, but it is a good proxy for the performance of a similar engines in the acceleration.
Other than that, torque is just a design parameter for the transmission.
If you have the whole graph of power vs vehicle speed at different gears, the maximal torque doesn't carry any meaning.
