If it's a well written story, it doesn't matter to me. I like them all!
I prefer short stories. I don't have time for novels online. There's too much to do online as well as in real life. I would rather read a really good short, than one that drones on and on.
Purveyor of Poetry & Porn
I'll read a multi-part story if it's by an author I like...but I prefer not to start the first chapter until I know the whole story is done...
I've seen people post a couple of chapters and then not finish the story until months later...or sometimes not at all in some cases...
Not a good thing...
When I have written continuations of stories, I try to make sure they stand up as stories in their own right, so that anyone can access them without having read the prequels. But then, people don't know that until they read it, so they're unlikely to jump into something labelled "Part 4".
In a way, you have to 'commit' to a story series. The first one has to really grip me if I'm going to continue reading. I don't mind if they drag on for a while if the quality of the writing is good and it remains captivating, like the Porn Star Dad saga, now nearing 20 installments and still a damn good read. Sometimes, it gives me something to look forward to. One of my favourite writers, SensualDesires83, often posts stories in multiple parts and I eagerly anticipate the next chapter.
At times, I do just fancy a quick, one-off story. It comes down to what you're in the mood for.