Well, it looks like a bunch of other people have explained much of this while I was writing, but here’s my two cents.
Race cars (the kinds you mention) have two types of “grip:” the tires’ grip and aerodynamic downforce created by wings and the car’s underbody, which has special venturi tunnels that create low pressure zones to suck the car down to the track. Ground effects methods were not unique to cars of the 1980s, but are essential to today’s open-wheel series. The techniques used are extremely sophisticated and in many cases are closely guarded secrets.
I’m assuming tire grip is a clear enough concept not to require explanation, and that your question was directed mostly at the cars’ aero features.
On superspeedways (e.g. Indianapolis, Fontana, etc.) which have long straights, teams do indeed reduce downforce, since moving in a straight line does not require much grip and downforce there only slows the car. At these tracks, banking in the turns helps make up for some of that lost grip.
But on road courses (twisty turny tracks, not ovals), downforce allows a car to go faster through curves and turns than the tires’ unassisted grip would permit. The higher ratio of curved track to straight track makes the trade-off between power and downforce worth it. In other words, they may be a little slower on the straights, but they’re faster overall, which is what counts.
An often cited, but still fascinating, fact is that Champ Cars have so much downforce that over 100 mph (and they can go almost 2.5 times that fast) they generate more downforce than their own weight. This means that they could theoretically run upside down “on the ceiling” at that speed. I really wish someone could arrange a real world demo of that.
BTW, I think you’re wrong about Champ Cars beating F1. When the Champ Cars ran in Montreal last year, it was the first time in decades that both series had run the same track. The F1 cars were about 5 seconds faster. The F1 cars have about 100 more horsepower, weigh 250 pounds less, and are permitted to use traction control and launch control.
I gotta run. There’s an Indy Racing League race on tonight.