It all depends on when you want to go, bear in mind that those are main tourist attractions, and if you are going on week-end days and the weather is good,you are in for long queues, either for the boat-trip to the Herrenchiemsee island (if that's your plan) as well as the eagles nest: you can only go up with a special bus and then it's a lift all the way up.

I don't know about option a), as for option b), it's an hour's drive from the Chsee to the Eagles nest, so I guess that if you only plan to see the lake from the shore and then go to the nest it would be ok. Only bear in mind that the last bus driving to the lift for the nest leaves at around 16.30, so I'd plann the timetable carefully.