Is the acceleration of car greater when hitting the accelerator, or the brakes? Is acceleration of car greater than when pedal the pushed to the floor or when break pedal is pushed hard? I do understand that the signs would change in either but I am more considered about the magnitude.... 
 A: The breaking system is nearly always more powerful than the engine.  This is a good thing, because you want to make sure you can stop as best as possible.
Theoretically both systems are limited by the friction of the tires.  If you have an engine which can cause your tires to slip as you accelerate, then both acceleration and breaking systems have the same limiting factor -- the tires.
However, most cars cannot break the tires free simply by pushing the pedal to the metal.  Those who wish to break the tires free (such as drifters), typically do so using other forces, such as forces generated by turning or through the clutch.
Consider this thought experiment.  (I say "thought experiment" rather than "do this" because of safety concerns!  Always stay in control of your vehicle!)  If you were to accelerate to say, 40mph, and then slam on the brakes, you could easily cause them to lock up.  This is why we have ABS brakes-- because its easy to lock up and lose control.  However, at 40mph, it is almost impossible to hit the gas and break the tires lose.
Go ahead and try the "hitting the gas" half of the experiment, where it is legal and safe.  You won't be able to brake the wheels free unless you have an enormously powerful car that you bought for the expressed intent of having that much power!
A: Assuming that you have enough of a variety of gear ratios available, every car should theoretically be able to "burn rubber" when accelerating, up to a certain critical speed $v_0$. On a level road, with the standard model of friction, $v_0=P/\mu_s mg$, where $P$ is the maximum power the engine can supply.
So below $v_0$, the acceleration you can get from the gas pedal or from braking is equal in magnitude, because it's limited by friction and equals $\mu_s g$. Above $v_0$, the brakes are always capable of a greater acceleration, because they are always capable of making the car start to skid, or of providing infinitesimally less friction that that, causing the car to have an acceleration equal to the frictional limit. (In modern cars, this capability may be hidden from you by antilock brakes. Studies with professional and ordinary drivers also show that ordinary drivers basically never brake as hard as their car is capable of doing without skidding.)
A: The breaking time and distance of a car are affected by many variables, such as road conditions, the condition of the brakes and the type and condition of the tires.  Also, of course, the reaction time of the driver and the vehicle speed. The accelerations of cars varies widely. 
In order to compare gas pedal acceleration to brake pedal deceleration, you would need reliable data (generated by an independent source) for the same car under the same conditions. But here are some general observations of mine. 
I read the typical braking distance of a car going at 60 mph (88 fps) once the brake pedal is pushed is about 180 feet. If I did my math correctly, that works out to a stopping time of about 2 seconds. That does not include the "thinking" distance of 60 feet (according to the source) which would of course increase the stopping time. The average deceleration of the vehicle would then be 88 ft/$s^2$
The 0-60 mph acceleration times for vehicles varies widely. For high performance cars I read they are typically less than 6 seconds, but then those cars typically have shorter stopping distances as well. In the case of exotic sports cars the the 0-60 times can be between 2.5 and 3 seconds. For them the acceleration and braking times (and thus magnitude of acceleration and deceleration) might be more comparable.
But for typical non performance cars (family sedans or SUVs) 0-60 times are greater than 6 seconds. So for them it would appear that 60-0 braking time would be less than 0-60 acceleration time, meaning the braking deceleration would be greater than the car acceleration, than would be the case for the exotic sports car.
Update:
It has been suggested that my answer left open the possibility that acceleration may be greater than braking. That was not my intent. I simply wanted to point out all the variables involved and the observation that the difference between braking and acceleration (e.g., the ratio of acceleration to braking) is generally less for a high performance car than for a typical family car. But braking still generally wins out.
