I'm an EU citizen considering to immigrate. Which country should I select Ireland or UK?

For cost of living data, see numbeo.com. You can also use their comparison feature to compare, say, Dublin v. London, or your own country v. Ireland and v. UK. Although you fail to state your citizenship, it's very likely that cost of living in either is much higher than your country, especially a place like London.

With Brexit still hanging over your head, UK is probably a bad choice. Unlikely you can remain. Both countries have job shortages, so unless you have really good skills in short supply in one country or another, expect difficulty finding work. UK is particularly overloaded with immigrants & illegal aliens, so finding work is tough. If you do not have a good education (at least bachelor's degree) plus experience in an occupation in short supply, you may have serious difficulties finding any work which pays enough to cover the most basic survival needs.

Your consideration option is only the Republic of Ireland as the UK is leaving the EU

The UK is leaving the EU so the only place that might take you is S. Ireland.