Jason,
I've needed to do this from time to time, and there isn't a particularly elegant way in Logic, but it can be done. (In ProTools you can just select samples for the timeline and highlight the distance to read the sample count directly... be nice if Logic had this feature...)
In Logic, I've solved this by cutting both regions to the first transient, then opening the region with the second transient in the sample editor. In the sample editor, you can measure the sample count directly by highlighting, so once the regions are cut to the first region's transient, you can highlight from the region start to the transient in the second region and that's your sample delay.
-James