The second runs in less than 20% of the time. Also of interest, the 2nd case has lots of notices about using summary search info in the job inspector. The first does not.
No, this isn't my actual use case. But it illustrates the problem I'm having using a saved search in a dashboard. It makes the acceleration useless because it takes so long to run.
Edit: The report acceleration summaries page does not increment the count in the case of search 1. Search 2 does. Based on the evidence, I'm thinking acceleration doesn't play with subsearches, joins or appends. Expected?