This is more a technical question than a historical one. There are many historical questions one could ask about either, but this is not really one of them.
Short answer:
Hiroshima involved a small amount of reacted material (fission products) released very high in the air, at a very high temperature. The result is there was almost no local fallout — the 1kg or so of fission products produced stayed high in the air for a long time, and had time to diffuse over a large area.
Chernobyl was a large amount of reacted material (reactors contain much more fuel than a bomb, and Chernobyl was at the end of its fuel load, so it had on the order of 100X more fission products released than the Hiroshima bomb), it was released at a low altitude (venting out the top of the reactor) at relatively low temperatures (enough to loft it, but it came down pretty quickly also). The result is a lot of local contamination with fission products.
One should not overestimate the radioactivity at Chernobyl today; radioactivity levels drop some 100X over the first 48 hours after something like this. You can visit the site, you can even work at it, without immediate health risks. Living there means chronic exposure over a long term, and that means increasing your chances of cancers and birth defects a bit. For an individual, it is not a huge risk increase (though some populations, like children, are more susceptible). But for a large group of people, a small increase in risk can translate into a lot of cancers.
Longer answers: see the many answers given at ELI5 or AskScience, where this comes up pretty frequently.
The most dangerous radioactive byproducts of nuclear reactors and bombs are fission products, and they are produced in proportion to the amount of energy produced by the fissioning device. The bomb that destroyed Hiroshima in 1945 released 15 kilotons (63 terajoules) of energy, and thus an equivalent amount of radioactive fallout.
Let's take a look at the RBMK-1000 reactor that exploded in the Chernobyl disaster. Those reactors are designed to produce 1000 megawatts (1 gigawatt) of electrical power, doing so by producing 3500 megawatts of thermal energy from fission reactions. Reactor number 4 at Chernobyl had been completed in 1983 and so it was in operation for approximately 3 years at the time it exploded. During that time it generated around 10.5 gigawatt-years of energy from fission reactions, or about 1.2 million terajoules. So you can see immediately that Chernobyl reactor number 4 contained at least 10,000 times the quantity of longer lived dangerous radioactive isotopes (fallout) than the Little Boy atomic bomb produced.
Additionally there are the dynamics of the situation. The Hiroshima bomb was an airburst, when the bomb went off it vaporized itself and deposited its energy into the nearby atmosphere, and it was primarily the energy (not the bomb fragments) which unleashed destructive power on the city. The vaporized fallout from the bomb mostly rose into the upper atmosphere on the rising hot air from the bomb blast and was dispersed into the stratosphere and then mixed into the atmosphere as a whole. What fallout did come back down soon after the blast had been vaporized so it was subsequently washed away by rains and significantly diluted over a fairly short period of time.
Compare this to the Chernobyl disaster. The reactor was blown apart and then was on fire for some time. This meant that large chunks and ash particles containing radioactive material were distributed around the nearby area. The danger in the exclusion zone is that you will run across one of these "hot bits" and either ingest it or breath it in, where it will do tremendous damage to you. Because these bits and pieces are things like dust, ash, and chunks of material they don't wash away so they are not substantially diluted or dispersed by the passage of time. If, perchance, you scrape off all of the surface material in the Chernobyl exclusion area and feed it into a massive ultra high temperature incinerator then you could render the area safe for habitation at the cost of very minutely ticking up the amount of background radiation experienced by everyone on Earth.
As a side note, these events also occurred at very different points along the timeline of consciousness concerning the hazards of radioactivity. Post-war 1945 Japan had a much different approach to radioactive hazards than the Soviet Union in the 1980s. A city that was destroyed by a nuclear bomb today would probably not be so cavalierly rebuilt and re-inhabited without extensive testing and remediation efforts as necessary, but in 1945 that wasn't really an option or a thought.
Hey gang; thanks for the thorough answers everyone