I am certainly not writing Besiktas off, but to be honest Fenerbahçe is currently the strongest team in the Turkish league. Besiktas made wonderful signings, but out of all those signings, only two players were in form last season (Trossard and Vlahaovic), I don't think the other signings are enough to rate them much higher.
Fenerbahçe has strengthened the squad in almost all positions, and I think they are worthy to be called title contenders for next season.
As for Besiktas, I would say we should watch out for them next season, they might contest for the title next season who knows, but I am sure they will do well compared to their last season performance.
For me, Fenerbahce is currently the team with the most desire and interest in finishing a championship in an absolutely positive way.
I absolutely wouldn't leave out Galatasaray because for me they are at the same level, while i see Besiktas as a team still in transition, trying to compete in a more decisive way, since they have made two important purchases in Trossard and Vlahovic.