It seems to me that they both measure the delay time of sinusoids passed through a filter.
- Am I correct in thinking this?
- If so, how do the two measurements differ?
- Could someone give an example of a situation in which one measurement would be more useful than the other?
Reading ahead in Julius Smith's Introduction to Digital Filters, I've found a situation where the two measurements at least give different results: affine-phase filters. That's a partial answer to my question, I guess.