Are you sure? They're both unvoiced th, which is what thorn is for if you intend to distinguish.

I can't tell whether Old English used eth for those words early on - though the unvoiced quality in modern English makes that seem unlikely. Did we also devoiced them? Eth died out fairly quickly in favour of thorn in all cases, voiced or not. Possibly because its name is "eþ" not "eð". It doesn't even use itself. (Though, ironically, 'w' also doesn't and it replaced ƿynn, which does.)

There was another commenter - actually might have been the same guy, I'm not all that sure - who did use eth for voiced instances, to similar controversial effect in comment sections.