Well, the Arlanda Express is fast (like Heathrow Express) and is SEK 300 for 2 passengers at the moment (the usual summer discount offer to 30th August), while Airportcab is SEK 475 to SEK 525 for up to 4 passengers from Arlanda (but only SEK 365 to SEK 390 in the other direction) . You must pre-book at least 3 hours before. At ARN you have 30 mins grace time and then it's an extra SEK 75 for each 30 minutes you are late.
There are other taxis that sometimes are cheaper (eg TaxiKurir is currently SEK 470 to/from ARN) and you can just get them from the taxi rank. The taxi will take you anywhere in the inner city (inom tull) whereas Arlanda Express will only take you to Central.
So it can very much depend where you are going to in Stockholm too.
Then there is the bus - Flygbussarna - which is generally the cheapest direct transport (currently SEK 99 per person) - and reasonably quick too - it has a few stops along the way to/from Central that are sometimes more convenient than Central.
But the cheapest of all is the public bus between ARN and nearby Märsta and the commuter train (pendeltåg) to/from Märsta (all done on the one ticket).
(I lived in Stockholm for 14 years).