Domestic partnership law parallels marriage law up to a point. The law that applies to your domestic partnership is the state in which the partnership has its locus. Let's say you elect to register in State X because it provides advantages over CA but you then live in CA, your rights and liabilities vis-a-vis one another would be governed by CA law, not that of state X. I hope this answers your question.
There are many legal complications to domestic partnership law still, and one of the complications is that, unlike marriage, D.P.'s are neither allowed in, nor recognized in, all 50 states.
A limited number of states have domestic partnerships; a slightly larger number will recognize the domestic partnerships from other states. Some states neither permit D.P.'s, nor recognize other states' D.P.'s, and, of course, right now, the Federal government really does not recognize D.P.'s as equivalent to marriage. To get an answer that will do you any good, you will need to speak to experienced family law attorneys in the specific states you're interested in learning about.