I've flown both. Ryanair basically has one pro - the price. Zero dollar airfares are cool - every time I flew them it was on a fare of less than $5 round-trip (taxes usually added about $40-50). A lot of newspapers and commentators compare them to Southwest, but they're actually much more of a low cost carrier than WN - dirt-cheap fares as I said, but even fewer amenities (e.g. charging for water, their in flight 'magazine' is just a catalog of junk you can buy on board, no connecting itineraries, tiny free checked luggage allowance that has now disappeared altogether).
One big difference: Southwest is known for exceptional customer service. Ryanair's CS is certainly exceptional -exceptionally bad.
I've wondered why someone hasn't tried starting something like FR here in the US - I'd think with the lower taxes here, their business model would be even more successful (obviously it would serve a specific niche of the market rather than the mainstream).
Yonatan