Aer Lingus IcelandAir

Both of them get you there; one with a connection in Dublin, the other with a connection in Reykjavik. Problem with either could be cancellation of the on-going flight.
You might check with UAL, which would give you a domestic connection in either ORD or IAD.
I'd take whichever flight has the least overall flight time end to end so you are not spending precious time waiting at an airport.

I haven't flown Icelandair since Covid but I had good experiences with them before. In economy you have to buy or bring aboard your food, unlike transatlantic flights on most other airlines. Reykavik is an easy connection, compact and well organized. I think you can add some time in Iceland if you want with no additional fare on Icelandair. Don't have experience with Aer Lingus.

One thing to consider is if you fly Aer Lingus via Dublin on your return you pre-clear US immigration in Dublin so upon arrival in Seattle you are in the domestic terminal. It’s been a while since I cleared immigration in seattle but my memory was that the line was endless.

I've flown Iceland Air several times. Pros are that the transfer in Iceland is extremely easy and efficient. There is a large difference between Saga Class and coach. You pay extra for most everything in coach and I would definitely pack a lunch/breakfast as the food in coach is not very good. Saga Class is the equivalent of domestic first class with larger more comfortable seats (not lie flat), good catering, and good service. It also comes with lounge access. If getting from point A to point B is your goal, then Iceland Air in coach can be an excellent bargain.

I have only flown Aer Lingus on a domestic flight before, but it was fine.

I would go with the one that seemed to have the best price overall.

edited to add: I've never spent more than 20 minutes going through border control in Seattle, but I think it has more to do with how many planes arrive at the same time as anything else. I have heard that extra time is required to go through border control in Dublin. I think you will be spending time on this. With one, it is after arrival and with the other it is during a connection.

second edit to add: You can earn frequent flier miles on Alaska Airlines Mileage Plan with both of these airlines.

Following up on A-A's suggestion that you consider contingency options in the case of missing a connection—Aer Lingus would be the clear winner. They'd have many more flights to the continent and could route you on their corporate-sibing airlines if necessary. Even if something to happen affecting your departures from Seatle or Frankfurt, they'd have countless options to route you with BA or AA.

Additionally in favor of Aer Lingus is that the long flight would be on a wide-body plane, arranges 2-4-2 in economy, which feels much more spacious and comfortable. Wheraes on Icelandair, you'd fly both segments on 3-3 single aisle narrowbodies.

I've flown Icelandair a few times the last time being a little over two weeks ago.

Transfering at Keflavik is like a well oiled machine. They are masters at it. I usually fly Saga so I can't comment on coach.

I've only flown Aer Lingus short haul so I can't comment on their long haul service.

I flew Iceland Air to Paris a few years ago. One benefit is it one of the quickest ways to get to Europe from the Pacific Northwest, I think the flight was around 7.5 hours from Pdx? And then a manageable hop to many cities on the continent. I just wish they had they had larger planes so we didn't have to sit 3 across.

I have flown Iceland Air six times, with the most recent trip being this past February. We have never had any issues on our flights, FWIW. The one thing though is leaving SEA, they do not staff their desk until a couple hours before the flight. So the line forms and gets VERY long as there are only a handful of agent desks there. Also note that even if you have Global, sometimes the TSA people will turn you away and make you go to the main TSA area. For whatever reason, they did that to us this winter even though our boarding passes cleared had it marked. But of course you cannot argue with the TSA people;) Upon landing back at SEA, the officials were at baggage claim with the beagles and sniffing all of the bags and talking to every person there. Just an FYI.

Thanks everyone. We decided to stick with Icelandair. Our next issue will be figuring out train schedules to get from Brussels to Luxembourg City. I have found the time schedule but have yet to find a map which shows where the stops are. Anyone where to find a map?

Maybe too late to add this comment, but I love Aer Lingus. I have traveled with them several times transatlantic, and they are now my preferred airline. The service has been great and, at least pre Covid the food was quite good. They don't offer a premium economy for extra legroom, but I fly from the east coast so the flights to Dublin are quite short
The only downside right now is the mess at Dublin airport.

I flew Aer Lingus last weekend from SFO-DUB. Hubby and I were able to sit in the 2 seats on the side without anyone next to us. Clearing passport control in Dublin was a breeze and our checked bags were just fine.