The eth/thorn distinction was fairly arbitrary in actual written Old English, with thorn being more common. The modern distinction between eth and thorn being based off of voice originated in Icelandic, I think? That's the only language that still uses them in its modern form, anyways.
I admit I'm only going off of Wikipedia, but that claims (in the "Old Norse" article) that extant writings from that period used thorn exclusively, and again the use of thorn and eth as the unvoiced and voiced variants is a relatively modern convention.
