For Multiclassing, combat maneuver degree is the primary advantage of Multiclassing.
In your example fighter has the better maneuver degree progression, so at level 6 you would have access to 2nd degree maneuvers.
Most other features are gained as per the class progression you gain a level in.
-You get 1 exertion pool, but bonus exertion generally stacks
- you gain access to traditions learned from both classes, plus any additional traditions from other sources like subclasses
- you get maneuvers know as you take a level in a class as per the level in that class, this can make maneuvers known progression a little wonky and can make it important as to when you take levels in a class.
Per your example if you take
2 levels in berserker first you would know 2x1st degree maneuvers,
At level 3 (2 berserker/1 fighter) you would learn 3 additional 1st degree maneuvers
Total 5 x 1st degree maneuvers
At level 4 (2 berserker/2 fighter) your maximum degree known would be 2nd and you would gain 1 x 2nd degree maneuver
Total
5 x 1st degree maneuvers
1 x 2nd degree maneuvers
At level 5 (2 berserker/3 fighter) nothing is gained
Total
5 x 1st degree maneuvers
1 x 2nd degree maneuvers
At level 6 (2 berserker/4 fighter) you learn an additional 2nd degree maneuver
Total
5 x 1st degree maneuvers
2 x 2nd degree maneuvers
I hope this clears up any confusion