Both exception and objection refer to a statement issued either verbally or in writing, in protest to actions of others.
At the outset, it must be made clear that there are two commonly used meaning of exception, while objection has only one meaning.
The everyday usage of the word exception includes meaning indicating that certain things are excluded from a categorization (such as with the exception of Sundays and holidays).
The strictly legal usage of “exception” is now to be compared with the usage of the word “objection”.
The more common of the two word is objection, while exception is old fashioned, and in some legal systems, it requires a specific legal action for the parties in disagreement with the decision of a court to retain a viability of an appeal on the issue.
I want to note an exception to your decision- a disagreement expressed in a special way.
I take exception to your statement – I disagree with what you say.
No one objected to the holding of a meeting – no one disagreed with the holding of a meeting.
The defendant's attorneys wishes to exclude testomony by objecting to the hearing of the witness.