How to implement contradictory comments/suggestions from collaborators?

I handle conflicting suggestions as follows: Consider all suggestions for this point, work out a suggestion based on the other suggestions and send an email to all collaborators and write something like "In this respect I got conflicting suggestions namely... I would suggest to proceed as follows... because... ".

It would be best to collect all the points of conflict in one message.

You may reduce the number of conflicts a bit by adding another step to your workflow: Before starting to write the paper have a session/discussion about the structure of the paper, its focus and the notation. This costs some time and be difficult, but can considerably reduce the number of conflicts. Especially you may point out that some issue has been already discussed in this session.

Oh, and by the way: I would not suggest to encourage all coauthors to cc their comments to the whole group of authors and have the discussion like that. Then the thread may loose focus pretty fast and things may get messy.

In some cases both co-authors can be right even if their suggestions are opposite: If a detail is included, it may be necessary to include further details, so either cut or expand. Which you do may depend on the journal you are targetting - you do have one in mind don't you? Some have a tight page limit and thus a lower expectation of the amount of background, while others expect everything to be fully explained. Some work may never fit in the former.