I'm a rare user of these platforms, but all I ever see is that I get an email with a link to sign something. Sometimes it's DocuSign and sometimes it's Adobe or something else, but I certainly don't feel any loyalty towards one over another, and as a signer, I certainly don't trust the platforms to hold onto my copy for me.

It seems that unless you've got clients who are trying to use DocuSign as their personal document management system, as long as the interaction flow is essentially the same it should be fine.