It's important to emphasize that there is a free market for taxis in Sweden. The general rule is to stick with the majors in any city, although there are a few that actually undercut the big companies. The independent and "other" companies will usually try to charge a lot more and essentially rip you off eventhough the fare is disclosed properly, etc. You are not compelled to select the first cab in a rank, but pick your choice of cab company.

In addition to the two already mentioned, the third major in Sthlm is 020 (yellow cars). So each one of these will have a similar flat rate to town. I guess you could try to negotiate with one of the other drivers.......

Here is a website where you can get prices for cabs:
http://iqtaxi.se/flygplats/taxi_arlanda_fran.php

If this is up to date then 020 has the best rate of the majors. Taxi Card always comes up as the cheapest, but I doubt that you'll find one Arlanda. They are not a "major" and I have never noticed one of their cars -- not that I am looking for them.