Well this is what Fedor's coaches said after he knocked out Arlovski
https://www.mmamania.com/2009/01/26/trainer-fedor-won-with-his-old-tricks-not-his-training
So the simplest and likely most accurate explanation is that Fedor didn't train seriously enough for his fights in strikeforce. As a consequence he made more mistakes in the fights and ended up losing.
On a more technical side, there are different ring generalship strategies when in a cage vs a ring. Take this image below
This can help explain some of the ring generalship tactics found in boxing, kickboxing, muay thai and mma in a ring. Firstly, the worst place to be is in the corners of C, and the best place to be is in the middle of the base of C (where A meets C).
As the fight starts, both fighters move towards region A. An infighter or slugger will want to back their opponent up to region C but will also settle for region B. Region B is a less useful place to put your opponent in because they have more room to move and can move into region C on either side, whereas when they are in region C they are trapped. So as a fight goes on there is a bit of a chess match going on if you have two intelligent fighters. Each wants their opponent in region C and each wants to avoid getting stuck in region C. They also know that their opponent wants the same thing. So part of the game is to try and outwit your opponent with footwork and strikes to get them trapped in region C without getting trapped their yourself.
With an octagon or cage (in its various shapes) there is much more room to move around. It is difficult to get trapped anywhere and it can also be difficult to cut off the cage because there really aren't any regions to trap a fighter. You could argue that being trapped along the cage is equivalent to getting trapped along the ropes. While this is true most mma fighters don't have a clue what to do when they get their opponent there. They should try and keep their opponent on the cage and make them feel trapped by knowing which exits they have and then cutting them off. Then they should us strikes to punish them for getting caught there. Something like staying in the center and keeping your opponent in the red triangles
So for Fedor the ring generalship tactics are different and that can make it difficult to strategize, which can result in a change in performance.