Ee-ther / Nee-ther mostly, I think I've said the other type too.
It's most likely a context thing. I know if I'm talking up a storm I'll likely be saying it as Ee-ther / Nee-ther.
I use both pronunciations regularly. I don't really know what makes me use one over the other at any given time...maybe it's based on my mood, the context, or the person I'm talking to. There are certain pronunciations that I believe I favor in certain phrases. I think I'm more likely to say "ee-ther way" and "eye-ther one", but I have no idea why.
I have found that we typically use both pronunciations for these words. I’ve noticed that throughout. My lifetime, but it is interesting to see that it’s the same around the world. (or at least in The Bell Tree community anyway, haha)