F1 as a sport, may have lost some of it glory with downsized engine and introduction of turbo. Increasing restrictions have left almost no room for engineers to play with. F1 car however, remains an epitome of engineering still, and can outperform any road car even at its worst. Unless you happen to own a Koenigsegg Regara or some other sports car, in that case, you should be able to come extremely close. So what are the differences between a road car and an F1 car?

Aerodynamics

A normal road going car is a bluff body in technical parlance, and has significant pressure drag associated with it. Attention is paid to effect of air flow and is studied only as much as to make sure that it does not affect the car-in-motion adversely. However, in case of an F1 car, aerodynamics play a much bigger role and the car is designed to take the benefit of the airflow around it.
An F1 car’s body is streamlined so that there’s minimal drag at high speeds. Not only that, aids like splitter, diffuser and wings etc. ensure that as speed increase, the down force on the cars increase and effectively the traction, braking force that can be applied and speeds that it can carry into corners increase too.

Engine

Engine of a road car is designed keeping in mind the reliability and robustness. So that, it lasts 15-20 years of long service life. As a result it’s heavier and produces power that much less in proportion to its weight. While an F1 engine not only produces more power, it does that at the absolute limit and the service life is not much of a concern. 
F1 Engine
According to Colin Chapman, “The ideal grand prix car would win a race and fall apart immediately after taking the chequered flag, having pushed every one of its mechanical tolerances to the absolute limit.” Therefore, every engine component is designed to ensure that it's performance is not limited by the extra weight.

Gearbox

Transmission
A road car utilizes any transmission of the type - manual gearbox, CVT, DSG, AMT, AT etc. The focus is again on reliability and longer service life while keeping the cost of upkeep low. Not in the case of an F1 car, that uses a sequential transmission, which may be as quick as the DSG transmission, which is considered quickest among road cars, but the weight and space saving is tremendous due to the absence of extra clutch and other components.

The paddle shifters in case of CVT and other transmissions in case of road cars, let you change gears mechanically as you would do in case of an F1. But gear changes are nowhere as quick as in the case of F1 which does in it roughly about 5-8ms.

Dynamics

All forces (steering, braking, acceleration etc.) on the car act via tires and for convenience it’s assumed that they act through the CG (centre of gravity) of the cars. In case of road cars, the position of CG is much farther from the ground, therefore the moment is also much higher. While an F1 car is extremely low slung and has a CG that's very close to ground helping efficient dynamics.

For this reason, a road car that’s built for convenience loses momentum in overcoming from reactions like pitching and rolling. While in case of an F1, along with lower CG, the damping is in the critical region to ensure that unsprung mass settles quickly and there’s minimal loss of traction. For this reason, the ride is extremely uncomfortable for the driver, but it aids all other aspects of car’s performance.

Braking performance

Unlike a road car that comes equipped with features like ABS, EBD etc, an F1 car lacks all sorts of driver’s aids. In case of road car, the focus is to improve active and passive safety for passengers and drivers, while in case of an F1 car it’s much to the skills of the driver and how he utilizes them to bring the car to a stop.

F1 brakes undergoing testing
The brakes in an F1 car however are much advanced and can withstand higher than normal temperatures without fading.

Acceleration performance

While a normal road car is meant to carry passengers from point A to B, an F1 car is meant to go around a track with highest speed possible. Since there are limited straights and track is composed of all sorts of section, it’s important that car does not only have sufficient top speed, it’s more important that it accelerates and achieves that speed quickly enough as it would need to shed the speed as it goes into a hair pin bend or a sharp corner.

An F1 car overtakes another car on track
An F1 car can typically accelerate from 0 to 100kmph in under 3 seconds, an average road car however may require around 8-12 seconds.

Wheels / Tyres

The greater the mass, the greater the force it requires to attain speeds and stopping. Therefore, the focus in case of an F1 car is to make everything as light as possible. Cost is not a limiting factor and wheels are generally made of magnesium to keep the unsprung mass low as it provides great balance between strength and weight.

F1 wheel
While in case of road cars, cost plays a major role and most road going cars use steel wheels or alloys to keep costs low. The tyres used in case of F1 cars are standardizied and provide impressive grip level, they can never last more than a single race session or even less, which is nothing in comparison to tyres that road cars use.