A radically different foundation legend to Irish Christianity, and quite possibly a far more Martinian flavour to its monasticism. The reduced contact with the Mediterranean flavours of monasticism may also reduce interest in and/or availability of some texts, but that is not likely to be a major issue yet (no, the Irish did not save civilisation, only Carolingian grammar).
An interesting question is to what extent irish Christianity OTL is British and to what extent OTL's British remnants were Hibernicised. I'll defer to experts to answer that, but with the British missionaries playing a larger role in Ireland, the result may be a more unified, possibly a more episcopal church.
Also, Irish missionaries would be fewer in number due to the absence of the Patrician legend and more deaths by snakebite. Interesting repercussions for the Picts and the Anglo-Saxon kingdoms later on.