Car "oomph": power or torque? Two of the most important magnitudes that characterize a car's engine are maximum power and maximum torque. How are those two magnitudes related to the sensation that the car has "oomph" or is "powerful" (in the common, wide sense of the word)?
I would tend to think it's the torque. My reasoning: Compare the same car model with different engines, but  with the same weight. We can assume the moment of inertia to be the same. Assuming also that the same gear is engaged, no tyre skidding etc, the engine with more torque will provide more acceleration.
However, car magazines and advertisements usually refer to power, rather than torque. So power somehow seems to be the important one?
 A: The torque and power curves are of course related (power is related to torque times RPM) but the maximum torque and maximum power are achieved at different RPMs and tell us different things about the car, therefore both are specified. 
Best is of course to look at a diagram like the one below, showing the relationships of the BMW 335i twin-turbo engine as an example:

The maximum power is usually achieved near the highest rated RPM for the engine, but since you normally don't drive the car near the max RPM, this figure by itself is less useful for the non-racing driver than looking at the torque curve I think. The maximum torque is usually achieved at a lower RPM so just getting that parameter (and the RPM it relates to) could be more useful actually.
You might be able to estimate that a car with a higher maximum power might have a higher torque at relevant RPMs of course so it's still useful for quick comparisons.
In a turbo engine (like the 335i engine above) the maximum torque will be very quickly achieved at low RPMs and it will then stay flat through a long range; this is where you typically will be driving the car between gearshifts and this is what will give you the "oomph".
A non-turbo engine will have a more gradually increasing torque curve.
But just to be clear, both parameters are related and similar engines with different maximum powers also probably have some similar relationship between their maximum torques (and oomphs).
A: Torque ($\tau$) and power ($P$) are mathematically related to each other:
$$P = \tau \omega$$
Where $\omega$ is the angular speed (effectively the RPM) of the engine.  Since the torque of an engine is a function of $\omega$, we can think of this as either
$$P(\omega) = \tau(\omega) \omega$$
Where $\tau(\omega)$ is some torque-speed curve dependent on the engine design, or 
$$\tau(\omega) = \frac{P(\omega)}{\omega}$$
If you have two different cars, both driving with the same RPM ($\omega$), and car A has 1.5 times more torque, it also is using 1.5 times more power.
A: *

*when people refer to a "powerful" car ... they actually mean acceleration. This means Torque (which gets translated to Force at the end of the drivetrain). And Force = m x a ... so for a given mass, Torque == Force == acceleration.

*Unfortunately, the technical definition of the term Power is defined as Torque x Revs. This means the Power curve is sort of redundant information. And, it does NOT equate to "powerful". Only the Torque curve does.

*Because of this muddled use of Power and powerful, the average Joe gets confused. However, because manufacturers don't handily display Torque curves (they generally tell you maximum Torque only), we can make use of the maximum Power figure to approximate what the Torque curve will look like: a low Power:Torque ratio implies the maximum Torque is occurring at low revs (and a high ratio means it occurs at high revs). It's not an exact science, but its a useful indicator when you only have two numbers to go on. 

*So .. your Torque curve is all that matters ... except that you need to modulate it by the gearing, so that at higher gears you get less torque at the back wheels. Also, there are friction forces that will slow you down, most notably wind resistance. It is proportional to the cube of velocity, so all cars will have a "terminal velocity" (or max speed) where the cubic curve crosses the gear-adjusted torque curve.

*FInally, remember that F = m x a ... so to get more a, reduce your m (mass). Go on a diet, take no passengers, have nothing in the boot, remove your seats, take out the a/c, and you get more ooomph :)
A: Power will tell you how fast you can go - without power you cannot overcome the drag (force of drag goes with $v^2$ so power needed goes as $v^3$). The torque is a measure of the instantaneous acceleration you can get - the ability to transfer power to the wheels. Note that acceleration also requires power - you are adding kinetic energy - but at lower speeds torque is king; at high speeds it's power.
So to feel "oomph" you need torque. To go fast, power.
