Both are possible and are fine. Also, "добрался" is possible, as mentioned in Artemix's and Herokiller's answers.
If you ask me how I would say it as a native speaker - I would say "добрался". More specifically, I would say: "Я добрался туда на самолёте". "Туда" (there, to that place) is not mandatory, but it sounds better that way.
Maybe I can say something about the slight difference between прилетел/долетел/добрался:
If you say прилетел - it's more like "I came/arrived (using an air transport) there by plane"
If you say долетел - it's more like "I made it to there (to Moscow) by plane"
With Добрался it has the same translation as with долетел, but долетел can be used onlywith air transport, and Добрался can be used with any means of travelling: car, train, plane, boat, even on foot.
Motion words with до- prefix have this sliiight shadow of meaning that you arrived and arrived successfully. For example, when I arrive somewhere by plane, I send an SMS to my family saying: "Я долетел". That way I slightly stress the fact that I made it by plane without accidents, in other words, that I didn't crash. 8)
Same works with приплыл/доплыл (if you're sailing), приехал/доехал (if you're driving or riding public transport or train), пришёл/дошёл (if you're on foot)