Should do both or just one and WHICH one? I have never been to Ireland and don't know if I'll be able to do both. I know Ring is more touristy - am I missing out if I only get to Dingle?

Do BOTH. They are entirely two different worlds. The ring of Kerry is a worthwhile tour. You will learn and see more if you take it in a small bus, & can see over the hedge rows, & can hear the history and stories about it. Then go to the Dingle and relax. It is not as touristy & has many friendly fine pubs and people along with a more quite setting. DO BOTH!