Update; I've been doing this a bit longer now, and I am even more inclined to be surgical. That is to say, I recommend flagging all the comments. Frequently I encounter situations where a subset of the comments are now redundant, but the complement of that subset are still valid. I'd rather not make that judgement on my own; I'd rather rely on the community to flag.
I may not be the ideal person to answer, because I have only been moderating for a week or two. I need to understand the context of the comment before acting. On the other hand, in my limited experience, context has not been a discriminator. That is to say if a comment needs to go, it needs to go. While I have consulted context, it hasn't been relevant.
The comments I've deleted have either crossed the line into acrimonious debate, (in which case I'm going to delete the comment without reference to context), or have digressed beyond the attempt to clarify the question - in which case I'm going to delete without reference to context.
That answer feels a bit like Tevyev from Fiddler on the Roof - "they're both right.", but like Tevyev, it is at least sincere.