They don't conflict; they were designed to work together. You can have schema.org (in JSON-LD, RDFa, or micro data) on the same page as Dublin Core, etc.
For example, there's no explicit property in schema's Person type [1] for a nickname. But the FOAF standard does [2].
Just add FOAF to the JSON-LD context:
{
"@context": {
"@vocab": "https://schema.org/",
"foaf": "http://xmlns.com/foaf/0.1/",
"pronouns": "https://schema.org/pronouns"
}
You now use the FOAF nickname property:
"@type": "Person",
"givenName": "Timothy",
"familyName": "Berners-Lee",
"foaf:nick": "TBL",
You can do the same thing with Dublin Core, DBPedia, etc.
[1]: https://schema.org/Person
[2]: https://xmlns.com/foaf/spec/#term_nick
To be fair schema.org and dublin core say “when a property is name ‘title’ it means …” and you can expect to find the following properties…
Json-ld says: if you want to know whether the “title” property means the schema.org or the dublin core variant then you can find out which it is by <json-ld algorithm>
So you’d always use json-ld _with_ schema.org or something.
I think if you are using Dublin Core, it’s because you’re a library. Maybe I am off the mark, but that is the sense I get from this—not all these standards should be used for all pages on the web.
I think you should just think about what metadata you actually care about, and the main metadata I care about (choose your own list) is authorship, publish date, last update, subject keywords, thumbnail (OpenGraph 1200x630), and summary.
There’s a long list of additional metadata that I could put in my webpages because there are standardized ways to do it, but, why bother?
There is also microformats.