EHIC and GHIC cards provide you with the same level of health cover as residents of the EU country that you're visiting get. The only real benefit of travel insurance (with regard to health cover) is that it includes repatriation costs. (e.g. if you needed an air ambulance to get you home from, say, Greece, travel insurance would normally cover it).
An existing EHIC remains valid until the expiry date printed on it. Thereafter you'll need a GHIC:
https://www.gov.uk/global-health-insurance-card
I wouldn't bother with travel insurance for a trip to Ireland unless I felt that I needed cover for any high-value belongings that I might be taking with me. I'd be prepared to trust that I could get free, or cheap, treatment if I fell ill or became injured, and that I could get home from Ireland under my own steam (or with the help of friends or family), without the need of an air ambulance or other specialist transport.