Raw horse power is not the definitive test of the speed. The Cosworth engine actually has the highest peak bhp figures of all of the engines on the grid, but it is by far and away the worst engine on the grid because of its poor driveability.
The modern cars do generate a lot less raw power than the turbo engines of the 80s but there are a lot of reasons as to why. For a start, the engines of today have to last a lot longer than they did back then 8 engines for the season. There was nothing in the rules to stop the teams from using a different engine for each session in the 80s, meaning that in qualifying in the 80s the cars would run an engine that would only last a few laps, but deliver much higher power, and then put a lower powered engine that would do a race distance for the race.
The cars of the 80s were very very inefficient compared to today's cars. The obvious difference is in the aerodynamics, with today's cars having less drag and more downforce - in fact, while F1 cars have long been able to theoretically drive upside down because their weight is greater than their downforce, the Red Bull could probably drive upside down with a 1980s car hanging from it the right way up, such is the difference in downforce (the Red Bull generates more than the weight of an F1 car more downforce than an HRT, and an HRT generates more downforce than the cars from the 80s)
With less drag that cars do not need as much power to accelerate faster, and the drag means they can corner much quicker. The power delivery is a lot more consistent, and the other big area of advance is the braking and tyre technology. Formula 1 cars now have such grippy tyres they can pull 6G under braking, and the brakes are so good they can do this lap after lap, corner after corner without suffering brake fade (unless you are a HRT at Montreal)
A modern Formula 1 car is an organic creature compared to the 1980s cars, meaning the packaging of the engine is integral to the design of the car (for example, when Brawn switched the Brawn to the Mercedes engine in 2009, a much much better engine in terms of power and driveability to the Honda engine it had been designed for, the car was arguably slower than it would have been with the Honda lump, they had to compromise the car's packaging to fit it in) so if you were to switch engines between cars from the 1980s and the current generation neither car would be faster. In fact, the modern car would probably not even last a race distance because the engine would be too tightly packaged, overheat and explode.
It would probably accelerate quicker with the increased power and torque, but once it got to corner the engine would be a lot heavier, with a higher centre of gravity and would compromise the car's handling.
It's worth noting that the cars of the 1980s had turbo chargers which enabled the high BHP figures, the naturally aspirated engines of the time were no where near the power levels, in fact, the 1992 Williams (a few years later) which had the best engine reached equivalent BHP with today's engines, but that was with a 3.5 litre engine, nearly 50% extra displacement, on an engine that could be thrown away after qualifying and the race.
The reason for this is that the cars could not rev anywhere near as high, we're talking about 12,000 rpm compares to 18,000 (which is now limited by regulations rather than technology - F1 cars were exceeding 20,000rpm before the cap was introduced) - when the new turbos come in, the cars will be limited to 15,000 rpm, however this compares to about 10,000rpm during the 1980s turbo era. The cars will be allowed max fuel flow from 10,000rpm, which means coupled with the turbo while the BHP figures might be lower than the current engines, they will probably have more torque, and torque is more important to acceleration than raw BHP.