I don't find Ryanair much cheaper than Aer Lingus. In my experience there's up to a 20% premium, and I just cross checked the Alicante route for next week with the same results.
Compared to the high likelihood of delays or cancelled flights with Ryanair, I think it's worth it for peace of mind.
As a bit of a bonus for the latter airline, you are permitted to yell "Forth Aer Lingus!" as you charge headlong towards your seat.
RyanAir is ultra-budget. You need to be ready for the whole thing, but often you can get something much cheaper. As an example, looking for London to Belfast next month, RyanAir is a fifth the price.
Aer Lingus is a slightly weird case; they have essentially become a budget airline (at least for their European business) to compete with Ryanair, but they haven't yet gotten around to adopting most of the dark patterns.