That answer above me from Ed P is possibly the most ill-informed answer i have ever read. How is there more skill involved in cornering a banked oval than a flat/undulating race track with changes in gradient, elevation, camber, corners with multiple apex, etc. As for doing nearly the same speed as an F1/indy car...ha! The busch series came to Montreal a few weeks ago and the lap times they were doing would have meant they were lapped every 2 1/2 laps and the champ cars used set slightly slower speeds than the f1 cars.
Formula 1 is the Worlds premier motorsport category comprising of 17-19 Grand prix at a range of different styled circuits all around the world. The circuits are all twisty road courses with no ovals on the calender. The drivers are all multi national with most coming from Europe or South America. The teams are made up of privateer teams(williams, spyker) or big companies like BMW, Ferrari, Honda, Toyota). Because the cars are built individually by the teams and are developed as the year goes on the the technology gets better every year and they keep getting faster.
The main difference with F1(and champ car which is the old indy series that has since split into two) is that they race on road courses. Road courses are acknowleged by anyone with sense to be a far more difficult proposition to drive than a banked oval with only 2, 3 or 4 identical corners. The laps in are much longer in f1 with the longest being about 4.5 miles and the shortest about 2.5(the old nurburgring used be 14miles long until it was deemed too dangerous). Oval circuits range from 0.5 to 2.66 miles long. There are only 2 road courses on the entire NASCAR season and many of the teams bring in road course specialists because sometimes their drivers are often quite a way off the pace when the course isnt an oval.
F1 cars are considerably faster than NASCARs or any other car on the planet for that matter. They are open topped and open wheeled. They accelerate quicker, slow better and corner better. They are essientially fighter planes on the ground. They have more technology in them and unfortunately have had Traction control for the last few years which is bad as it limits the drivers input and bad drivers dont get punished as much. From next year on though there will be no traction control as it has been banned so we will be able to see who really are the good drivers. The cars do not have slick tyres(threadless) anymore so they are not as grippy as they used be. This was a poor attempt to slow the cars down but failed as the cars were faster despite being narrower and with slower tyres the next year. The FIA(governing body) are always bringing in rules to keep the cars slowed but these rarely work as the engineers will always find a way to gain whatever they have lost. This has led to poor racing as the cars are unable to follow each other closely in corners because the wind left behind by the leading car upsets the aerodynamic balance of the following car. F1 car engines are also tightly regulated. This year they are 2.4 litre normally aspirited engines producing about 800hp. For the previous 10 years the were 3.0litres and produced up to 1000hp. They are very light(about 95kg) and advanced.
NASCAR engines are much heavier and produce much less power relative to their aspiration. They are roughly 5.7 litre engines and put out about 800hp.
NASCARs are heavy, relatively slow and poor handling. They are much stronger and can take a lot more damage. They look more like a regular car but are completly unrelated to any car you will drive.
F1 drivers have to be better conditioned as the cockpit is so small they have to be small to fit into it. Alex Wurz at 6'3" is considered very large and is the biggest driver in F1 but he is still athletic. The cars take much more physical activity to drive them. The drivers have to turn both directions while all the time countering the tendancy of the car to slide out from under them. The drivers have to put up with much higher leteral G-forces putting huge strains on their neck and go very hard over bump kerbs which can be a foot high. F1 cars suspension is much stiffer so they feel every single bump in the cars and some of the tracks like brazil are extremely bumpy, you can see the drivers head getting thrown about. The cars also get very hot as all the airflow is directed over the drivers head and into the air vents. The huge brakes which reach 1000c are at all four corners and the engine is at his back all making it very hot and uncomfortable.
NASCARs have banking to help them around the corners. As much as the people here like to tell you how amazingly fit nascar drivers are they are in nowhere near the same league as f1 drivers. Many of them are overweight like tony stewart and they are able to race for much longer careers as it is less physically demanding. Montoya is an ex f1 driver who moved to NASCAR and he has put on a lot of weight since he left f1, in fac he would not fit in an F1 car anymore. NASCAR drivers have good arm strength and can handle heat well but are not overly athletic otherwise.
NASCAR races tend to be longer and have numerous caution periods which bunches the field up close. In F1 this only happens occassionally as when there is an accident the drivers continue at race speed. This means that the driver/car that has been fastest all weekend generally wins unlike in NASCAR where it is impossible to pull out a good advantage as the pace car will bring them all back together and then there is a lot of luck involved in with not getting caught in a wreck.
NASCAR is now the pinnacle of american motorsport but it does not get much attention outside of america although with the arrival of Villeneuve and Montoya that will change as i know many people who have become a little bit interested since they moved. The racing is much closer and yes it is more competitive as there are more cars that are capable of winning the race. In most f1 races only 4-5 cars can realistically win the race. Nowadays F1 has become very boring as the governing body has made a complete mess of regulating it and the tight aero rules make overtaking almost impossible unless one car is considerably faster than the other and there is much justifiable criticism that the cars are now too easy to drive as they have so much grip but there are plans to change this and as ive said TC is being banned. That said F1 cars are much harder to find the limit of. Villeneuve drove a nascar for the first time in his career this week and after 70 laps was within a 0.3secs of the time set by his championship leading team mate. Jeff Gordan drove an F1 car( although it wasnt set up for testing to get the best time as it was a promotional thing) and his fastest lap was 9 seconds off the pace Montoya set in that car earlier in the year.
On the other hand many people find NASCAR very dull as the circuits are so boring as they only turn left and have no nice scenery, elevation changes or breathtaking corners. NASCAR is great as long as you have a driver to support otherwise its pretty dull as all the overtaking moves are identical.
As regards INDY...it is a mess these days. The old CART championship which used have the Indy 500 is now gone and has split into IRL and Champ car world series. Now they are splitting american open wheel racing into two seperate groups and there is not enough support to sustain them both. The cars in IRL are like F1 cars but not quite as fast around a road circuit. They also race on ovals like NASCAR but at far higher speeds and is much more dagerous as contact between wheels can lead to a major accident.
NASCAR - american only closed wheel, full bodied stock car racing on ovals
F1 - internattional race series on road courses and the pinnacle of technology
IRL/Champ car - american based open wheel series that will be lucky to survive the next 5 years if they dont rejoin together.