I've read series straight through, and I've read them with other books in between. I think I like the second option the best.
I read the two Thomas Covenant trilogies straight through. I was exhausted at the end. Well, those are exhausting books, anyway, but still, I don't think I would have had the same reaction to them if I'd read them one at a time, over a longer period of time.
On the other hand, I read Donaldson's two-book series, "The Mirror of Her Dreams" and "A Man Rides Through", as they came out, with other books in between, and that was quite a satisfactory way of approaching them. I don't think anything was lost by doing that. I also read Tim Powers' semi-trilogy consisting of "Last Call", "Expiration Date", and "Earthquake Weather" over a period of time, with other books between, although on a much shorter timeline than I did "Mirror" and "Man". This also did not hamper my enjoyment of them.
And then there is Kage Baker's novels of the Company. I've read this series three or four times, at least. The first time, I read them with other books between. Then I read them right in a row. Maybe it was because it was the first read-through, but I have to say that I enjoyed them more with some time between the books.
So, now I am reading "Outlander". There are, what, four sequels? I am enjoying it so much that my first impulse is to go out and get the others and read them straight through. But I don't think I'll do that. (For one thing, I can't afford to go out and buy all of them at once.) I'll let one digest a bit before I tackle another. If I can find the restraint.