you are already guilty of a lazy stereotype...
I'll assume you mean 'culture' in the socio-anthropological sense and compare the two as they scored in the international values survey pioneered by Geert Hofstede
Anyway, in turns of comparative values, according to Hofstede's framework Ireland and the UK are overall pretty similar with significant differences in just 2 of the 6 dimensions measured
individualism - Ireland is about two standard deviations below the UK (meaning they're traditionally have bigger families and group loyalties are a little more important)
long term orientation - Ireland is about two standard deviations below the UK (meaning that the Irish value (religious) Truth over secular Virtue and are more interested in the past and present rather than in making longterm plans for the future.
where I would expect Ireland to differ (Uncertainty avoidance) due to Ireland's catholic past.... they have the same scores.
So... a little different, hardly completely different.