Really, it varies from paper to paper, and giving you a story count could be misleading. Two of the papers I worked on had very tight news holes and management at both placed a premium on editing so not an inch was wasted; we spent much of our time squeezing every bit of fat out of copy, when we trimmed we were not lopping off paragraphs but tightening sentence by sentence, removing unnecessary words and phrases, sometimes with such finesse that writers couldn't always tell 15 percent of the story was gone. That kind of editing takes time. You might only edit eight stories, but you were doing major work on all of them.
Some large papers have only a couple of editions, some have quite a few, and you might be updating constantly. It would not be unusual to edit a staff-written pro file three times, a plugger for the early edition, running for the next edition, and a writethrough with quotes for the next.
Some papers zone heavily and some don't. On one that zones a lot, the same story might have different lengths and different hed specs for multiple editions.
The amount of deadline copy can vary from market to market. It is one thing to work in a market that has one MLB team, one NFL team, one NBA team and one NHL team, and it is quite another to work in a market that has two of each. You might not be very busy for much of the shift, but you need X number of bodies for the flood of deadline copy.
The most prestigious newspaper on my resume was where I worked the hardest. Standards were high, there was a lot of fact-checking expected. There were seven editions. We zoned the preps. We had to cut most staff-written copy, sometimes by quite a bit. We didn't just choose a wire story, we took AP, KR, LAT-WP, etc., and merged them together to basically recraft it into a a story that combined the best elements of each. We ran a lot of breakout graphics, and the idea was not to create one that dupicated the story but something that complemented it. So the "duty roster" might have only eight items per person on it, but we were busy all night long.
Another factor is that a good sports desk is a lot like communism: from each according to his abilities, to each according to his needs. Meaning the workload won't be even. If you are fast, you might generally be assigned more work than the person sitting beside you. If you are going to work on an extremely complex story or design an extremely complex page, you might be assigned fewer files. I'm very fast, for example, but when there was a story that might take half a shift because it was very long and contained the potential for a lawsuit, well, I'd get fewer files so I could give that monster the extra care it needed.
In short I disagree that your workload decreases when you move from a small paper to a big one. It may look that way if you go strictly by story/page counts, but if you are not trying to work at a progressively higher level and make it more difficult, you are cheating your employer, your readers and worst of all yourself. I found it got harder and harder as I moved to larger papers. You can skate by or you can push yourself, and if you want to reach your potential you will push yourself.