I can only answer the first part of your question in the case of Irish and how it compared to Welsh. I focus on the historical and sociolinguistic reasons for its decline and survival, which are intertwined with English rule. Someone else may have a more comprehensive answer but this might shed some light on some of the broader considerations in your question.

Firstly though, Irish didn’t die out. It came close but didn’t ever completely disappear. There may not be any monolingual speakers in the present day but bilingual speakers do continue to use Irish and have done throughout the centuries, just in decreasing numbers. At present, according to the 2016 Census, just over 78,000 people speak Irish in Ireland on a daily basis outside of the education system. In terms of Scottish Gaelic, the 2011 Census records 57,602 members of the Gaelic language community (1.1% of the total population). In contrast, the last native Manx speaker died in the 1970s and Cornish in the 18th century and both are now classed as ‘heritage languages’. It’s therefore difficult to compare them to Irish or to Gaelic. It also means I can't quite answer your question!

In the case of Irish, the spread of English had been happening since Henry II’s arrival in Ireland in 1171, but the political, economic and religious pressures of the 17th and 18th centuries (including the Penal Laws) really damaged the social standing of Irish and made English the language of the government, courts of law, authorities, civil service and upper levels of commercial life.^(1) The 19th century was particularly critical for Irish as well as Welsh, with both seeing growth in the spread of English, so I’m going to discuss a few key factors from that period:

Following the Act of Union in 1800, the new state accelerated language shift in Ireland because the Union afforded opportunities through the medium of English. The National School System (established in Ireland in 1831) taught solely through English, while political activists (e.g. Daniel O’Connell) and the Catholic Church operated through the medium of English too. The Great Famine was a watershed: it further accelerated the shift to English through deaths - as Irish-speaking areas on the western seaboard were disproportionately affected - and through emigration to English-speaking countries, primarily the US and Britain. Emigration played a huge part in the decline of Irish. It confirmed the relationship between the Irish language and poverty as there existed a correlation between those districts which were impoverished, those which were still Irish-speaking after 1850, and those which saw the greatest flow of out-migration; by the later 19th century, a culture of emigration was well established in Ireland and there existed a demand for English on the part of Irish-speakers, particularly the younger generation.^(2) On the other hand, emigration from Wales was less extensive and long-lasting, partly owing to the industrialisation of south Wales which enabled the surplus rural population to be absorbed internally, to a degree, and because the population was smaller. This meant that entire generations weren’t preparing for their inevitable emigration to English-speaking countries, as was the case in Ireland in the post-Famine period.^(3)

This all meant that while an estimated 60% of the population spoke Irish as a first language at the beginning of the 1800s, by 1901 this had fallen to 14.4%, of which just 0.5% were Irish-only speakers.^(4) In the case of Welsh, it was also the main spoken language at the outset of the 19th century. In 1801, 95% of the population spoke Welsh, with seven in ten being monoglots (i.e. Welsh-only). In 1901, 34.8% were bilingual and 15.1% were Welsh monoglots. In 1911 44.6% of the population spoke Welsh, of whom 8.7% were monolingual, and the majority of whom were old or middle-aged.^(5) In both countries, there were areas with much higher concentrations of Welsh speakers - usually rural, more isolated places. The important difference here is the percentage of monoglots: in Ireland, it has been proven that Irish as a primary language survived in the 20th century in those areas that had a high proportion of monoglots in 1891^(6), so it stands to reason that Welsh, with a greater number of monoglots, statistically had a better chance of survival.

Welsh had a rich cutural heritage - various activities were practised through the medium of Welsh, in particular religious practice through Welsh churches and celebrations like the Eisteddfod. In contrast,the first Oireachtas na Gaeilge (based on the Eisteddfod) was only held in 1897 and the church in Ireland did not have any centralised policy or support for the Irish language. Church affairs were officially carried out in English except where Latin would be the normal language, while Catholic priests were not educated in the Irish language.^(7) Another related and important factor is the prevalence of print culture in Welsh and the lack thereof in Irish. Institutional support from churches and the religious nature of print culture was crucial for sustaining print culture in Welsh (as well as Breton and Scottish Gaelic). This then extended beyond the religious realm and encouraged a secular printing culture and, in turn, continued literacy in Welsh. In 1896 there were up to 10,000 Welsh-language titles in print compared to Ireland’s 150 in Irish, and dozens of Welsh newspapers and periodicals, compared to just one in Irish. Niall Ó Ciosáin has convincingly argued that it was the Catholic Church in Ireland’s lack of support for Irish language printing that was central to both 19th-century literacy levels and language shift: while readers in Welsh had reading material, there was none in Ireland and the population were encouraged to read only in English, thus discouraging the use of Irish.^(8)

In brief: in the 19th century, the numbers of monoglot speakers, the effects of emigration and contemporary attitudes, and the existence of vernacular print cultures and cultural activities all played a role in the subsequent survival and/or revival of Irish and Welsh.

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In terms of the second part of your question, I’m unfamiliar with the revival of Welsh but it seems, from Wikipedia, that attitudes changed during the 20th century and positive steps were taken to support the language and its community - e.g. Plaid Cymru, language acts, broadcasting. While both Irish and Welsh came to be associated with backwardness, to varying degrees, in the 19th century, Irish seems to have struggled more to shift this perception. The Gaelic Revival (c.1890-1910) managed to improve contemporary attitudes to some extent but few positive steps were taken thereafter. One of the big things in Ireland is the fact that Irish was made compulsory in schools under the new Free State Government in 1922. This hasn’t gone down well, largely owing to the makeup of the curriculum, and has made many, many people resent the language.

References:

In my reply