Exterior breaker doesn't match interior

Is it acceptable to have a larger breaker at the exterior disconnect and a smaller breaker on the inside panel? Is it acceptable to have a smaller breaker on the exterior disconnect and a larger disconnect breaker in the inside panel? We run into both. I.e. 150 amp disconnect exterior and a 100 disconnect in the main panel. Or vice versa. We see this frequently when there are solar panels on the roof. We have received conflicting answers from electricians.

In general with the scenario of a the 100 amp exterior service disconnect and a 150 amp breaker in the panel there is no issue. The feeder is protected at 100 amps and the 150 amp breaker is just a disconnecting means.

In the reverse scenario there may be an issue with the 150 amp outside and the 100 amp inside depending on the size of the conductors between the two. I’m not sure if PV installations would change anything.