Adamant is generally the better Nature because it builds on Scyther's key Stat, Attack, while Serious is not a very good Nature on most 'Mons, considering it builds on every Stat at once at lower efficiency. If you're doing a casual run, farming the correct Nature isn't needed unless the game is getting pretty rough. Still, Adamant is a better choice for a Scyther, in-game or competitively.
Source: Experience. I've used Scyther/Scizor a lot both in Showdown! and just in general.