The answer to this question depends on how you measure it. If you measure it by GDP per capita, then the UK is richer than Ireland. If you measure it by purchasing power, then Ireland is richer. If you measure it by GDP, then both countries are about the same.
The UK has a GDP per capita of $50,910, which is more than three times the Irish GDP per capita of $15,836. The UK GDP per capita is also more than double the GDP per capita of the Republic of Ireland.
In fact, the UK has a GDP per capita of more than $100,000, which is more than double the GDP per capita of the Republic of Ireland.