Having utilized both the FlyBus and Airport Express, I'd choose AE every time. I've used their services for tours and airport transportation on two visits to Iceland. The service and staff are always courteous, knowledgeable, on time, have lovely and clean vehicles (Mercedes & Volvo), and are always a good value. They've created a 'hub and spokes' system so that all passengers can be picked up efficiently and taken to the central bus hub for transport. It's a very good method and it works. This airport service is cheaper than all other transportation and takes you right to the Icelandair check-in counter. If you book an airport round-trip and do it on line ahead of time, you can save even more money.Compared to other similar operations in Reykjavik, this one is a 5-star company.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.