Hi Wex,
I don't use BNA so I can't really help you over the differences/similarities issue. I have a Pro membership on FindMyPast and that gives me access to the complete newspaper collection. The new(ish) search function on FindMyPast allows you to set fairly precise search parameters, and one thing that you might appreciate is that you can set the search to specifically look at Irish sources. That said, the results can be very inaccurate. For example, even if you put "George Bernard Shaw" in apostrophes you would still get lots of results which only had two out of the three names. And you would also get results where Bernard Shaw appeared in one sentence or paragraph, and George Smith appeared in the next and so on. I can't comment on whether the OCR is better or worse than BNA, or indeed how good it is just on FindMyPast, because there doesn't seem to be any way of seeing the results it missed. That said I have found it is pretty accurate even on really poor quality scans.
I find the snippet feature on FindMyPast very useful. This allows you to select just the article or part of it, and download it as a good quality image which has the title and date of publication of the newspaper etc as the file title.
FindMyPast have a pretty good help desk staffed by humans, so you might try asking them about the BNA and FindMyPast question.