What is the difference between these two ways of searching for Catholic parish records (particularly as the latter is free and the former isn't)?
There are a few areas where the coverage differs - the first is by date RootsIreland covers some later dates, many of the NLI films cut-off around 1880. The second is locations - RootsIreland doesn't cover some areas - e.g. South West Cork, only a few parishes in Wexford, no coverage in Kerry, limited coverage in Co. Dubln, just 1 parish in Dublin city etc..
If I was searching for a record in a parish covered by both sites I'd start with FMP - I prefer the search which permits wildcards, and also allows selection of several parishes in one search so you can check adjacent parishes in one step.
Rootsireland has come along a lot to be fair to it and it also includes a lot of Church of Ireland and some presbyterian records (and some lovely Armagh Prerogative Court Marriage Licenses). I fear that sites like FMP contribute a little to religious myopia. I've found religion can be quite fluid in many cases.
That said, the standard of the transcriptions is diabolical in many parishes (right down to not even noting the parish or the denomination) and the absence of a wildcard search function is still a problem.
I'd echo Shane and add that there may still want to try Roots Ireland but FMP is certainly a friendlier place to start and there's loads of lovely stuff up there too.