Solution 1:

If you're creating a neologism, I'd say go with the one that sounds the best.

The -hood suffix, to me, sounds more general and impersonal (or universal) while -ship sounds more personal. But that is entirely my own feeling.

Dictionary.com lists -hood as being "formerly used in the formation of nouns," so if you believe that means it isn't used anymore on new terms then that's an answer of a sort. But I think you're free to do what you wish. Hey, it's your word.

By the way, what's the word you want to create?

Solution 2:

-hood denotes a state of being. -ship denotes an occupation or capability. They're related, yes, but I don't see them as synonymous.

For example, while it's not a standard word, I can readily assign a meaning to apprenticehood: it's the state of being an apprentice. You serve an apprenticeship during your apprenticehood.